Answer:
[tex]\text{\bf{D.}} \quad\sin^2{x}\sec^2{x}+1=\tan^2{x}\csc^2{x}[/tex]
Step-by-step 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
