Question

Which of the following is an identity?

Answer 1

`\text{\bf{D.}} \quad\sin^2{x}\sec^2{x}+1=\tan^2{x}\csc^2{x}`

Explanation:

It can be useful to write each of these in terms of sine and cosine. Of course the relationship between sine and cosine is ...

sin²x + cos²x = 1 . . . . . eliminates choice B

A: (1/sin +cos/sin)² = ((1+cos)/sin)² ≠ 1

C: 1/sin² +(cos/sin)² = (1+cos²)/sin² ≠ 1

D: sin²(1/cos²) +1 = (sin²+cos²)/cos² = 1/cos² . . . (left side)

(sin/cos)²(1/sin²) = 1/cos² . . . (right side)

left side = right side, so this is an identity