# Math

Prove the identity

csc^2x = 2sec2x / sec2x - 1

Sorry i really tried. I got : LS = 1 - (cos^2x/sin^2x) but that's it. please help

1. 👍 0
2. 👎 0
3. 👁 155
1. multiply RS top and bottom by cos2x and you have

2/(1-cos2x)
= 2/(1-(cos^2 x - sin^2 x))
= 2/(1-cos^2 x + sin^2x)
= 2/(2sin^2 x)
= 1/sin^2 x
= csc^2 x

1. 👍 0
2. 👎 0
posted by Steve

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To analyze the given text passage, I will first describe its content structure and then provide the required analysis.

The text passage contains a trigonometric identity to prove and a solution provided by a user named Steve. The identity is: csc^2x = 2sec2x / (sec2x - 1).

**Content Structure:**
- The passage starts with a request to prove a trigonometric identity.
- The user provides their attempt at solving the problem.
- Another user (Steve) provides a detailed solution to the identity.

**Analysis:**
single_question_with_answer

the passage contains a single mathematical question (to prove the identity) and a complete answer provided by steve.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Math

Prove the identity

csc^2x = 2sec2x / sec2x - 1

Sorry i really tried. I got : LS = 1 - (cos^2x/sin^2x) but that's it. please help

1. 👍 0
2. 👎 0
3. 👁 155
1. multiply RS top and bottom by cos2x and you have

2/(1-cos2x)
= 2/(1-(cos^2 x - sin^2 x))
= 2/(1-cos^2 x + sin^2x)
= 2/(2sin^2 x)
= 1/sin^2 x
= csc^2 x

1. 👍 0
2. 👎 0
posted by Steve

## Similar Questions

1. ### Math

Prove this identity 1. csc^2(pi/2-x)=1+sin^2xcsc^2(pi/2-x) 2. tan(pi/4+x)+tan(pi/4-x)=2sec2x

2. ### trig

prove the identity: csc x-1/csc x+1 = cot^x/csc^x+2 csc x+1

asked by shela on December 16, 2010
3. ### Trig verifying identities

I am having trouble with this problem. sec^2(pi/2-x)-1= cot ^2x I got : By cofunction identity sec(90 degrees - x) = csc x secx csc-1 = cot^2x Then split sec x and csc-1 into two fractions and multiplied both numerator and

asked by Hutch on March 9, 2015
4. ### Prove trig identity

Prove the following trigonometric identity: (sec^2x-1)(csc^2x-1)=1

asked by Randy on January 9, 2011
5. ### MATH

prove the identity: cos(x)*csc(x)*tan(x)=1

asked by Alisa on November 6, 2014
1. ### Calculus

prove if an identity csc (x)-cot (x)=sin (x)/1+cos(x)

asked by Anonymous on October 15, 2018
2. ### precalc

prove the identity (1 + tan x) / sin x = csc x + sec x

asked by clarice on October 13, 2015
3. ### Pre-Calc/Math

Prove identity: (sec x/csc x) + (sin x/cos x)=(2/cot x)
user
To analyze the given text passage, I will first describe its content structure and then provide the required analysis.

The text passage contains a trigonometric identity to prove and a solution provided by a user named Steve. The identity is: csc^2x = 2sec2x / (sec2x - 1).

**Content Structure:**
- The passage starts with a request to prove a trigonometric identity.
- The user provides their attempt at solving the problem.
- Another user (Steve) provides a detailed solution to the identity.

**Analysis:**
TYPE: SINGLE_QUESTION_WITH_ANSWER

The passage contains a single mathematical question (to prove the identity) and a complete answer provided by Steve.