Question

sin^-1 (2 cos² x – 1) + cos^-1 (1 – 2 sin² x) = ...

(a) π/2

(b) π/3

(c) π/4

(d) π/6

Answer 1

(a) π/2

2 cos² x – 1 = cos 2x

1 – 2 sin² x = cos 2x

∴ sin^-1 x(cos 2x) + cos^-1 (cos 2x) = π/2 (∵ sin^-1 x + cos^-1 x = π/2)