Prove:1/sin²A-1/tan²A=1​

Answers

Answer 1

Step-by-step explanation:

1/sin^2A -cos^2A/sin^2 A. ~tan = sin/cos

(1-cos^2)/sin^2A. ~ take lcm

sin^2A/sin^ A. ~ 1-cos^2A = sin^2A

1

for more free ans check bio

Answer 2

Answer:

[tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\tan^2x}=1[/tex]

Step-by-step explanation:

Prove that:

[tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\tan^2x}=1[/tex]

Recall that by definition:

[tex]\displaystyle \tan x=\frac{\sin x}{\cos x}[/tex]

Therefore,

[tex]\displaystyle \tan^2x=\left (\frac{\sin^2x}{\cos^2x}\right)^2=\frac{\sin^2x}{\cos^2x}[/tex]

Substitute [tex]\displaystyle \tan^2x=\frac{\sin^2x}{\cos^2x}[/tex] into [tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\tan^2x}=1[/tex]:

[tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\frac{\sin^2x}{\cos^2x}}=1[/tex]

Simplify:

[tex]\displaystyle \frac{1}{\sin^2x}-\frac{\cos^2x}{\sin^2x}=1[/tex]

Combine like terms:

[tex]\displaystyle \frac{1-\cos^2x}{\sin^2x}=1[/tex]

Recall the following Pythagorean Identity:

[tex]\sin^2x+\cos^2x=1[/tex] (derived from the Pythagorean Theorem)

Subtract [tex]\cos^2x[/tex] from both sides:

[tex]\sin^2=1-\cos^2x[/tex]

Finish by substituting [tex]\sin^2=1-\cos^2x[/tex] into [tex]\displaystyle \frac{1-\cos^2x}{\sin^2x}=1[/tex]:

[tex]\displaystyle \frac{\sin^2x}{\sin^2x}=1,\\\\1=1\:\boxed{\checkmark\text{ True}}[/tex]


Related Questions

What is an expression involving division that is equivalent to the expression below?
2/9 x 3/4

Answers

Answer:

2/9 ÷ 4/3

Step-by-step explanation:

Hi!! Can you please help with this question and explain how to solve it??
Find the height in centimeters of a square pyramid with a volume of 144 cm3 and a base edge length equal to the height. Give the approximate answer rounded to 2 decimal places.

Answers

9514 1404 393

Answer:

  7.56 cm

Step-by-step explanation:

The volume is given by the formula ...

  V = 1/3b²h . . . . where b is the base edge length, and h is the height.

Here we have V = 144 cm³, and b = h. Filling in these values and solving for h, we get ...

  144 cm³ = 1/3h³

  432 cm³ = h³

  h = ∛432 cm ≈ 7.55953 cm

The height of the pyramid is about 7.56 cm.

Answer:

[tex]7.56cm[/tex]

Step-by-step explanation:

Given that,

base length = Height

so,

[tex]volume = \frac{1}{3} {b}^{2} h \\ [/tex]

We can also write this as( according to this question)

[tex]v = \frac{1}{3} \times {b}^{2} \times b \\ v = \frac{ {b}^{3} }{3} [/tex]

let's solve

[tex]v = \frac{ {b}^{3} }{3} \\ 144 = \frac{ {b}^{3} }{3} \\ 144 \times 3 = {b}^{3} \\43 2 = {b}^{3} \\ \sqrt[3]{432} = b \\ b = 7.55[/tex]

[tex]base = height = 7.55cm \\ [/tex]

= 7.56cm

Is -6/11 a irrational number?

Answers

Answer:

No

Step-by-step explanation:

One way to tell if a number is rational is if it can be written as a fraction. Anything that can be written as a fraction of two integers is rational.

-6/11 is a fraction with integer numerators and denominators.

Therefore it is rational.

Uploaded this one again! Hopefully y’all can see it better

Answers

i believe it is 53.7

3.) Find the measure of the missing angle X:

120°
70°

Answers

Answer:

x=50

Step-by-step explanation:

Let's look at the red angle. if a flat line makes the angle 180, and the outer angle is 120, subtract 120 from 180. This will give you 60. Now every angle of a triangle added together will give you the sum of 180. So you already have 60 and 70, which make 130 all together. Subract 130 from 180 - (180-130) - and you'll get the result of 50.

The solution is :  the measure of the missing angle X is x=50.

What is an angle?

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

from the given diagram, we get,

Let's look at the red angle.

if a flat line makes the angle 180, and the outer angle is 120,

subtract 120 from 180.

This will give you 60.

Now every angle of a triangle added together will give you the sum of 180.

So you already have 60 and 70,

which make 130 all together.

Subtract 130 from 180

i.e. (180-130) = 50

and we get the result of 50.

Hence, The solution is :  the measure of the missing angle X is x=50.

To learn more on angle click:

brainly.com/question/28451077

#SPJ2

The equation y=1/4x represents a proportional relationship. What is the constant of proportionality?

A. 1/4
B. x
C. 0
D. 4

Answers

Answer:

k = 1/4

Step-by-step explanation:

A proportional relationship is

y = kx  where k is the constant of proportionality

y = 1/4x

k = 1/4

Answer:

a. 1/4

Step-by-step explanation:

1/4 shows the relation of y and x. (that y is one fourth of x)

Help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

The first statement is incorrect

Step-by-step explanation:

1 1/5 is positive so it is greater than the negative numbers

-2 2/5 is more negative than -1 3/5 so it is to the left on the number line

-2 2/5 < -1 3/5 < 1 1/5

11/5  < -2 1/5 is not correct  because 1 is bigger than -2

Answer:

1 1/5 < -2 2/5 because 1 1/5 is located to the right of -2 2/5 on the number line.

Step-by-step explanation:

Next time, don’t title your question like that.

This statement is not true because 1 1/5 > -2 2/5 because 1 1/5 is positive.

If m = 8 and n = 5, then man + 3) – n+1-

Answers

Answer:

P (−1)n(n+1)(n+2) (n+1)3 converges

Step-by-step explanation:

22. Find the area of circle with radius 7cm ( π) ​

Answers

Answer:

Sol:Here

Radius (R) =7cm

Area of circle (A) =pie*r^2

=22/7*7^2

=3.14*7^2

=3.14*49

=153.86

Answer:

A=49πcm²

Step-by-step explanation:

A=πr²

Given r=7,A=π(7²)=49πcm²

Help, I need this answered soon

Answers

Answer:

9.

Step-by-step explanation:

45 / [8(5 - 4) - 3]

= 45 / (8 * 1 - 3)

= 45 / (8 - 3)

= 45 / 5

= 9.

Hope this helps!

9

Work:
PEMDAS
45/8 (5 - 4) - 3
45/8 (1) - 3
45/8 - 3
45/5
9

Pls answer all questions

Answers

5:-c

The 3multiples are 25,50,75

6:-c

[tex]\\ \sf\longmapsto 6\:of\:2+9-5[/tex]

[tex]\\ \sf\longmapsto 6(11-5)[/tex]

[tex]\\ \sf\longmapsto 6(6)[/tex]

[tex]\\ \sf\longmapsto 36[/tex]

7:-a

12,17

8:-c

22=2×1188=2×2×2×11

HCF=2×2×11=44

9:-c

LCM of 9 and 5 is 45 hence its true

10:-c

HCF of two consecutive numbers is 1

cho tam giác ABC cân tại A trung tuyến AM.Biết BC=6cm,AM=4cm .Tính độ dài các cạnh AB và AC

Answers

Vì tam giác ABC cân tại A (gt) mà AM là đg trung tuyến nên AM đồng thời là đg cao của t/giác đó:

AM là trung tuyến của t/giác ABC nên M là trung điểm BC:

=> BM =BC/2 =6:2=3(cm)

Xét tam giác AMB vuông tại M

AB^2 =AM^2+BM^2 ( theo định lý Py-ta -go)

find a number such that when 3/4 of it is added to 3½the sum is the same as when 2/3 of it is subtracted from 6½. PLEASE HELP​

Answers

Answer:

- 120

Step-by-step explanation:

call x is the number you want to find

(3/4 )x + 3[tex]\frac{1}{2}[/tex] = (2/3)x - 6[tex]\frac{1}{2}[/tex](3/4)x + (7/2) = (2/3)x - (13/2)(3/4)x - (2/3)x = - (13 /2) - (7/2)(1/12)x = -10x = -10 / (1/12) = -120

Find the arc length of the partial circle.

Answers

Answer:

arc length = 4π units

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{90}{360}[/tex]

     = 2π × 8 × [tex]\frac{1}{4}[/tex]

     = 2π × 2

    = 4π units ← exact answer

Mark Brainliest please

Answer : Arc length (L) = 12.56637

What is the volume of a sphere with a diameter of 7.7 ft, rounded to the nearest tenth
of a cubic foot?

Answers

Step-by-step explanation:

V=4/3πr^3

V=4/3π(3.85)^3

V=4/3π(57.066625)

V=4/3 (179.280089865)

V=239.04011982

V=239 ft^3

change 0.625 to a percentage

Answers

Im pretty sure that its 62.5%

Answer:

62%

Step-by-step explanation:

If you need to round to nearest percent it will be 63%

Given that Ray B A bisects ∠DBC, which statement must be true?

Answers

B is the midpoint of DC.

What was the most common rating in the 26-35 age group?
nal
Is
OA Excellent
ОВ.
Good
OC. Average
OD
Poor
O E both Average and Poor

Answers

Answer:

I think its average

Step-by-step explanation:

not sure:)

Answer: it is average

Step-by-step explanation: just done It

Express 4 in simplest radical form.

Answers

Answer:

2

Step-by-step explanation:

PLEASEE HELP ASAP........

Answers

Answer:

(C). 126

Step-by-step explanation:

[tex]\frac{45}{x}[/tex] = [tex]\frac{65}{182}[/tex]

x = 126

Answer:

Hello,

Answer C\\

Step-by-step explanation:

Triangle EUT is similar to triangle EGF

[tex]\dfrac{EU}{EG} =\dfrac{ET}{EF} \\\\\dfrac{140-90}{140} =\dfrac{45}{EF} \\\\\\EF=\dfrac{45*140}{50} \\\\\\RF=126\\\\Answer\ C\\[/tex]

Use the table to find an quadratic equation of best fit.

Answers

Answer:

[tex]y = 5 {x} + 1[/tex]

when x is 0:

y = 5(0) + 1

y = 1 ( 5th box )

when x is 1:

y = 5(1)+1

y = 6 ( 6th box )

hence true for other values

Answer:

y=0.6x2+5x+1.1

Step-by-step explanation:

gjtgdgjdgdjxjfsbgsyuahjduegd love

A measuring cylinder of radius 3cm contains water to a height of 49cm. if this water is poured into a similar cylinder of radius 7cm, what will be the height of the water column​

Answers

Hey there! I'm happy to help!

Hey there! I'm happy to help!

First, let's find the area of the circle of the first cylinder. To do this, we square the radius and multiply by 3.14.

3²=9

9×3.14=28.26

Now we multiply by our height of 49 cm to see how much water there is.

28.26×49=1384.74

Now, let's find the area of the circle of the 7 cm cylinder.

7²=49

49×3.14=153.86

Now, we will take our liquid amount (volume) and divide by this circle amount (base) to find the number of centimeters of height of the water column.

1384.74÷153.86=9

So, the height of our water column will be 9 cm.

Have a wonderful day and keep on learning! :D

Ratios, Rates, and Percents
17:30
Question 16
Problem
Patricia traveled an average speed of 65 miles per hour for 4.5 hours and then traveled at an average speed of 60 miles per hour for 1.5 hours. What was the total distance in
miles that Patricia traveled during this time?

Answers

Answer:

382.5 :)

Step-by-step explanation:

took test

please please please help me with this assignment :)

Answers

Answer:

$45.63

Step-by-step explanation:

[tex]50,145 cm^{3} * 2.6 g/cm^3 = 130,377 g\\130,377 g = 130.377 kg\\130.377 kg * $0.35/kg = $45.63\\[/tex]

or all together    

50,145 cm³  *  2.6 g/cm³ * 0.35/kg =  $45.63

Please help ME ASAP!!Please explain the answer

Answers

Answer:

It seems like you misunderstood the instructions, though I don't blame you because they wrote it strangely. I believe that you're supposed to draw your own conclusion and then explain how you go there, rather than analyze a conclusion that was already drawn for you. If a long drive=a large fare, and you've been told that the driver has a long drive, you can draw the conclusion that "The fare will be large."

intergrate x×(x²-3)³

Answers

Answer:   [tex]\large \boldsymbol{\dfrac{1}{8 } (x^2-3)^4+c}[/tex]

Step-by-step explanation:

[tex]\displaystyle \large \boldsymbol{} \int\limits {x(x^2-3)^2 } \, dx =\int\limits \frac{1}{2} {} \, (x^2-3)' (x^2-3)^3 dx =\frac{1}{8} (x^2-3)^4+c[/tex]

Please help me solving this problem.

Answers

(a) The radius of the circle is the distance the wave travels since it first formed, so if g(t) is the radius of the circle at time t, then it changes at a rate according to

dg/dt = 60 cm/s

Integrate both sides with respect to t to solve for g :

∫ dg/dt dt = ∫ (60 cm/s) dt

g(t) = (60 cm/s) t + C

but C = 0 since the radius at t = 0 must be 0.

g(t) = (60 cm/s) t

(b) The area of any circle with radius r is πr ². So

f(r) = πr ²

(c) The composition of f with g represents the area of water encircled by the wave at time t :

(f o g)(t) = f(g(t)) = π g(t) ²

what is the answer to -3/7 x -1 2/3

Answers

Answer:

-9x-35/21

Step-by-step explanation:

Answer:

[tex]\frac{5}{7}[/tex]

Step-by-step explanation:

[tex]\frac{-3}{7}* (-1\frac{2}{3})=\frac{-3}{7}*\frac{-5}{3}\\\\= \frac{5}{7}[/tex]

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
The interquartile range is determined by the formula _____________.
A. Third quartile – First quartile
B. Third quartile + first quartile
C. First quartile – third quartile
D. Maximum – minimum

Answers

Answer:

A-Third quartile-First quartile

Step-by-step explanation:

The interquartile range is found by taking the third quartile minus the first quartile. It is also found by taking the right side of the box in a box and whisker plot and subtracting the left side of the box in a box and whisker plot

use an algebraic equation to find the measures of the two angles described below. begin by letting x represent the degree measure of the angles supplement.

the measure of the angle is twenty-nine times greater than its supplement

Answers

X+29x= 180
30x= 180
One angle is 6 the other is 174
Other Questions
If there are:6 red marbles10 yellow marbles5 green marblesand 1 blue marble What is the probability of picking 1 blue marble and 1 green marble? (Once a marble is chosen it is NOT put back into the box). (Write your answer in the form of a decimal, round to 2 places). One directionisthenewsingingsong Three blocks are shown. Which statement is correct?A. Block A has the greatest densityB. Block B has the greatest densityC. The density of Block A is equal to the density of Block BD. The density of Block B is equal to the density of Block C Which of the following is considered a Time/Temperature control for safety (TCS) food? Solve for x. Leave your answer in simplest radical form. Which relation is also a function please help me guys im desprate at this point What physical property can help characterize fragments of glass at a crime scene? Help me pls ASAP I WILL GIVE BRAINLIEST-3 = -e/75 Help ASAP 15 PointsA student is conducting their science experiment on the effect of caffeine on dogs. He has 3 groups of test subjects. The 1st group of dogs receives plain water. The 2nd group of dogs receives 10 mg of caffeine each, and the 3rd group receives 50 mg of caffeine each. He will measure their activity levels by recording how long each dog runs without stopping, after giving them the pills. What could be evaluated in this experiment to ensure reliability? A. The different amounts of caffeine given could lead to different activity levels which would throw off the result of the experiment. B. The group that receives water will be an outlier and throw off the best fit line. C. The test subjects are dogs and not people, so their data is unreliable. D. If the dogs are different breeds, their activity levels could be different because of their breed and not the caffeine. Reset Selection Why did the German Empire collapse? Ruth was slowly walking to her class. She was extremely tense about the math test. As she was walking she found a piece of paper on the floor. It was the math test with all the answers. Her heart skipped a beat. Ruth even though she was unprepared for the test returned the paper to her teacher. The teacher was happy with Ruths honesty. Ruth stammered, I Ive read the paper, and I know all the answers. Juanita is deciding whether to buy a dress that she wants, as well as where to buy it. Three stores carry the same dress, but it is more convenient for Juanita to get to some stores than others. For example, she can go to her local store, located 15 minutes away from where she works, and pay a marked-up price of $124 for the dress: Store (Minutes) Travel Time Each Way Price of a Skirt (Dollars per skirt)Local Department Store 15 102Across Town 30 85Neighboring City 60 76Assume that Juanita takes opportunity costs and the price of the suit into consideration when she shops. Juanita will minimize the cost of the suit if she buys it from the:______. . the average American student is in class 330 minutes a day how many hours is this You are trying to persuade members of your class to volunteer to tutor underprivileged children Is it Ethos, Pathos, or Logos and why. What is the standard form for the quadratic function? g(x)=(x6)25 Change the following into indirect speech a Dinesh said to his friends,"Who went to muktinath for worshipping the God?" Bone is flexible in nature. true or false. I bought this radio _rs 1000 a leaking tap drops water at the rate of 3 drops every second.each drop is approximately 1 ml. how many liters of water will leak from the tap during a day?a. 5 litersb. 50 litersc.500 litersd.15 liters