Question

Which equation is not an identity?

(A.) tan(–t) = –tan t
(B.) tan t(csc t + cot t) = sec t + 1
(C.) sin tcot t = cos t
(D.) cos2t − sin2t = –1

Answer 1

(D.) cos²(t) − sin²(t) = –1

Explanation:

The "Pythagorean identity" for sine and cosine is ...

cos²(t) + sin²(t) = 1

Changing the sign makes it not be an identity.

_____

A makes use of the fact that tangent is an odd function.

B makes use of cot=1/tan and tan=sec/csc.

C makes use of cot=cos/sin.

D has no relation to any definition or identity.