Prove that: (1 + cos A)^2 - (1 - cos A)^2/
sin^2 A=
4cosec A. cotA​

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

cosec x = [tex]\frac{1}{sinx}[/tex] , cot x = [tex]\frac{cosx}{sinx}[/tex]

Consider the left side

[tex]\frac{(1+cosA)^2-(1-cosA)^2}{sin^2A}[/tex] ← expand and simplify numerator

= [tex]\frac{1+2cosA+cos^2A-(1-2cosA+cos^2A}{sin^2A}[/tex]

= [tex]\frac{1+2cosA+cos^2A-1+2cosA-cos^2A}{sin^2A}[/tex]

= [tex]\frac{4cosA}{sin^2A}[/tex]

= 4 × [tex]\frac{1}{sinA}[/tex] × [tex]\frac{cosA}{sinA}[/tex]

= 4cosecAcotA

= right side,  thus proven


Related Questions

I HAVE UNTIL 3:30 PLZ HELPPPP 40 POINTS AND BRAINLIEST
Jake needs to buy 120 beverages for a party. Juices come in 8-packs and water comes in 12-packs.

Select all the pairs that represent a combination of juice and water that Jake can buy.

A (0, 10)

B (12, 2)

C (–2, 11)

D (, 5)

E (30, –10)

its linear equation for graphing.

Answers

Answer:

the ones you can use are A,B and E

Step-by-step explanation:

Plug each one in and find out if it works or not

Find the value of f(-2)​

Answers

Answer:

y = 3.5

Step-by-step explanation:

If you look at the x axis, you know x = -2 so you want to know y.

Use the graph to determine which statement describes f(x)
O A. f(x) does not have an inverse function, because its graph fails the
horizontal line test.
O B. f(x) has an inverse function, because its graph passes the
horizontal line test.
C. f(x) has an inverse function, because its graph passes the vertical
line test.
D. f(x) does not have an inverse function, because its graph fails the
vertical line test.

Answers

Answer:

f(x) does not have an inverse function, because its graph fails the horizontal line test. ⇒ A

Step-by-step explanation:

The vertical line test is used to show that the graph represents a

function or not

If the vertical line crosses the graph in more than one point, then the graph does not represent a functionIf the vertical line crosses the graph in only one point in different positions, then the graph represents a function

The horizontal line test is used to show that the function has an

inverse or not

If the horizontal line crosses the graph of a function in more than one point, then the function has no inverseIf the horizontal line crosses the graph of a function in only one point in different positions, then the function has an inverse

Let us look at the given graph

→ The graph represents a parabola, which represents the function f(x)

∵ Any horizontal line drawn will cross the graph in more than one point

∴ f(x) has no inverse

f(x) does not have an inverse function, because its graph fails the

  horizontal line test.

Twice a number y is no more than 12.

Answers

5? 5 times 5 is 10, which is less than 12

Helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp[[[[[[[[[Erica deposited $450 in a bank account at the beginning of the month. A payment of $35.20 is automatically deducted each month for her gym membership. If she makes no other deposits or withdrawals, how much money is in Erica’s account at the end of four months?

Answers

Erica will have $309.2 left in her mani account after 4 months
Answer:
$309.20

Explanation:
We know that..
- Erica started off with $450 in her bank account
- $35.20 gets taken out of her bank account every month

Using this information, we can write an equation:
E = 450-35.2m

E= the amount of money Erica has
m= the number of months that pass

And now, all we have to do is substitute m as 4 to find out how much money is in Erica’s account after 4 months.

E = 450-35.2m
E=450-35.2(4)
E=309.2

Therefore, there would be $309.20 left in Erica’s bank account after 4 months.

Write the equation of the line that is parallel to y=3x+1 that passes through (2,3)

Answers

Answer:

Y=3X+3

Step-by-step explanation:

Y=mx+b

m=3

when x=2 and y=3 b=3

Ashley has a $80 gift card to her favorite coffee shop. Each day, she uses her gift card to buy the a coffee for $4.50. Aaron has a $60 gift card to the same coffee shop. Each day, he uses his gift card to buy an iced tea for $2.50. For what number of drinks purchased will Ashley's gift card balance be equal to Aaron's?

A)9 drinks
B)10 drinks
C)
D)11 drinks 12 drinks

Answers

Answer:

The answer is B

Helps me solve this problem please

Answers

Answer: 1, 3, 5, 6

Step-by-step explanation: There cannot be the same x value for more than 1 y value.

Find the inverse function of
y =x-5/6

Answers

[tex]f(x) = y = x - \frac{5}{6} \\ [/tex]

Subtract the sides of the equation plus 5/6

[tex]y + \frac{5}{6} = x \\ [/tex]

So ;

[tex] {f}^{ - 1}(x) = x + \frac{5}{6} \\ [/tex]

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

not sure I need to answer two questions before I ask another question lol

12 divided by 3 +6 times 2 simplified

Answers

Answer:

16

Step-by-step explanation:

12/3 +6×2

4+12=16

Hope it helps

how could knowing the awsener to 72 divied by 8 help solve 7.2 divied by 8?
i really need help

Answers

7.2 divided by 8 is 0.9

Answer:

0.9

Step-by-step explanation:

72÷8= 9

7.2÷8=0.9

if you add a decimal ur answer is going to have a decimal

in this case 7.2 the decimal is in the tenths place so the answer would be 0.9

!/8 pound of fertilizer covers 25 square feet of ground, how much fertilizer, in pounds, is needed to cover 1 square foot ground?

Answers

Answer:

1/200 pounds

Step-by-step explanation:

Given ratio

1/8 pound ⇔ 25 square feet

To find

x ⇔ 1 square foot

Divide both sides by 25

1/8÷25 pounds ⇔ 25÷25 square feet1/200 pounds ⇔ 1 square foot


A hot air balloon rose from a height of 100 meters to 450 meters in 3
minutes. What was the balloon's rate of change

Answers

Answer:

350 meters.

Step-by-step explanation:

What is the slope given: (-1, 1) and (6, -1)

Answers

Answer:

m=-2/7

Step-by-step explanation:

Answer: -2/7

Step-by-step explanation:

uhhh not sure i just used math lol

Please please please help me

Answers

Answer:

131

Step-by-step explanation:

A straight line is 180 degrees and you already have 49 given, so subtract that from 180 and that gives 131 for the congruent angle

What is the value of 5 - 12?

Answers

Answer:

-7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

5-12=-7

hope this helps lol

7. Mark needs to move to a new apartment and is trying to find the most affordable moving truck. He will only need to truck for one day. After checking the U-Haul website, he finds that he can rent a 10 - ft truck for $20.95 a day plus $1.89 per mile. He then checks the Public Storage website and finds the charge to be $37.95 a
day plus $1.19 per mile for the same size truck. Determine the number of miles for which the cost to rent from either company would be the same. Round the answer to the nearest mile (5 points).

Answers

Answer:

24 miles

Step-by-step explanation:

Let the number of miles = x.

U-Haul:

1.89x + 20.95

Public Storage:

1.19x + 37.95

Set the costs equal and solve for the mileage, x.

1.89x + 20.95 = 1.19x + 37.95

0.7x = 17

x = 24.29

Answer: 24 miles

Help please!!!!!!! URGENT

Answers

Answer:

nvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

Step-by-step explanation:

cgfgbgfgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg

Solve for s.
2-2s=3/4s +13
s=​

Answers

Answer: s=-4

Simplify both sides of the equation and isolate the variable.

7x-130=110+9x. show with steps

Answers

Answer:

x=-120

Step-by-step explanation:

7x-130=110+9x

add 130 to both sides of the equation

7x-130+130=110+9x+130

Simplify

7x=9x+240

Subtract 9x from both sides

7x-9x=9x+240-9x

Simplify

-2x=240

divide both sides by -2

-2/-2=240/-2

simplify

x=-120

7x-130=110+9x
-7x -7x
-130=110+2x
-110 -110
-240=2x
2 2
-120=X

philp wrote an integer that is less than -2 greater than -3.5 which integer did he write

Answers

Answer:

-3

Step-by-step explanation:

Answer:

<-2, >-3.5

You can't really explain this without the chart that they probably gave you

-20xp + 15m -35p
Could someone help me

Answers

Answer:

5(-4xp+3m-7p)

Step-by-step explanation:

If the question is to factor the expression as much as possible, that's the answer.

12 is 90% of what number? Round to the tenth is necessary.

Answers

Answer:

12 is 90% of 13.33.

Step-by-step explanation:

What is the angle pair relationship between angles 6 and 8?

Answers

Answer:

Two angles are complementary angles if the sum of their measures is 908.

Each angle is the complement of the other. Two angles are supplementary

angles if the sum of their measures is 1808. Each angle is the supplement of

the other.

Complementary angles and supplementary angles can be adjacent angles

or nonadjacent angles. Adjacent angles are two angles that share a common

vertex and side, but have no common interior points.

Step-by-step explanation:

it easy

determine if the equation is true x = 8
2x - 6 = 9

Answers

Answer:

False

Step-by-step explanation:

This is false because:

1) In order to solve this, we cam use the addition property of equality

2) First, you can add 6 to -6 and 9

New Equation: 2x = 15

3) Now divide 2 with 2 and 15

New Equation: x = 7.5

You can also check by inserting 8 into the equation.

2(8) - 6 = 9

16 - 6 = 9, this is not true.

Therefore, this statement is false. x = 7.5

Hope this helps! :D

I don’t understand helpppp

Answers

Answer:

No

Step-by-step explanation:

I solved it and it didn't get 1 for any of them

Why don't churches use WiFi?

Answers

Answer:

becuase it is evil

Step-by-step explanation:

the will be evil and will become bad :)

why is math hard and important​

Answers

Answer: Math seems difficult because it takes time and energy. Many people don't experience sufficient time to "get" math lessons, and they fall behind as the teacher moves on. Many move on to study more complex concepts with a shaky foundation. And then often end up with a weak structure that is doomed to collapse at some point.

Step-by-step explanation: math is important because some things in math are gonna be used in your daily life for example adding, subtracting, division Etc and also because Math helps us think analytically and have better reasoning abilities. Analytical thinking refers to the ability to think critically about the world around us. Analytical and reasoning skills are essential because they help us solve problems and look for solutions.

hope this helps

Answer:

Math is very hard, but it will benefit you later in life because you learn certain material that can help you in the real world. It's an extremely important subject

Step-by-step explanation:

I NEED HELP ON THIS PLEASE!!

Below are the test scores for Ms. Brown's 1st and 2nd period math classes. Analyze the data and choose EACH correct statement:

1st period (Class A): 10, 15, 20, 25, 30, 35, 40

2nd period (Class B): 7, 12, 17, 25, 33, 38, 43

The standard deviation for Class A is 10

The standard deviation for Class B is 12.615

These are the options:

- The mean (average) score for each class is the SAME.

-The mean (average) score for each class is DIFFERENT.

- The variance for Class A is 125.

- The variance for Class B is 159.14.

- Class A has a greater spread.

- Class B has a greater spread.

- Based on the data, a score of 8 is more likely in Class B than Class A.

- If graphed, Class B would look more like the red graph below and Class A would look more like the blue one.

Answers

Answer:

hope that helps

Step-by-step explanation:

- If graphed, Class B would look more like the red graph below and Class A would look more like the blue one.

- Based on the data, a score of 8 is more likely in Class B than Class A.

- Class A has a greater spread.

Can someone answer this what do I put

Answers

Answer:

Where is the screenshot... I have to much free time

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