Question

Which of the following are identities? Check all that apply. A. sin^2x - cos^2x = 1 B. sin^2x = 1 - cos^2x C. tan^2x = 1 + sec^2x D. cot^2x = csc^2x - 1

Answer 1

Answer:

Option B and D are correct

Step-by-step explanation:

Option A is incorrect because the  correct  identity we have is

$sin^2x+cos^2x=1$  

Hence, Option A is incorrect

Option B is correct because we have an identity

$sin^2x+cos^2x=1$  

$\Rightarrow sin^2x=1-cos^2x$  

Hence, Option B is correct

Option C  is incorrect because we have an identity

$tan^2x+1=sec^2x$    not  $tan^2x=1+sec^2x$

Hence, Option C is incorrect

Option D is correct because we have an identity

$1+cot^2x=cosec^2x$   which implies $cot^2x=cosec^2x-1$  

Hence, Option D is correct.

Answer 2

Hey! The correct identities are: 1 + tan^2x = sec^2x 1 + cot^2x = csc^2x sin^2x + cos^2x = 1 which correspond to B and D