Which of the following is not an identity?

A. cos^2 x csc x - csc x = - sin x

B. sin x (cot x + tan x) = sec x

C. cos^2 x - sin^2 x = 1 - 2sin^2 x

D. csc^2 x + sec^2 x = 1

A) cos² x · 1 / sin x - 1 / sin x = - sin x

cos² x - 1 / sin x = - sin x

- sin² x / sin x = - sin x

- sin x = - sin x (correct)

B) sin x (cos x / sin x + sin x / cos x) = 1 / cos x

sin x · (cos² x + sin²x) / sin x cos x = 1 / cos x

sin x · 1 / sin x cos x = 1 / cos x

1 / cos x = 1 / cos x (correct)

C) cos² x - sin² x = 1 - 2 sin² x

1 - sin² x - sin² x = 1 - 2 sin² x

1 - 2 sin² x = 1 - 2 sin² x (correct)

D) 1/sin²x + 1 / cos²x = 1

cos²x + sin² x / sin² x cos² x = 1

1 / cos² x sin² x = 1

cos²x sin² x ≠ 1

Answer: D) is not an identity.