Question

Which of the following are identities? Check all that apply. A. cot2x + 1 = csc2x B. tan2x = 1 - sec2x C. sin2x = 1 + cos2x D. sin2x + cos2x = 1

Answer 1

I'll assume those are squares.  We know D is an identity:

$\sin^2 x + \cos ^2 x = 1$

Dividing through by $\sin ^2 x$

$1 + \cot^2 x = \csc^2 x$

That's A.

Dividing the original through by $\cos ^2 x$

$\tan^2 x + 1 = \sec^2 x$

Not quite B, wrong sign on tangent.  

C has the wrong sign on cosine squared as well.

Identities: A & D