Question

If (sin^-1x)² (cos^-1x)² = a ; 0 < x < 1, a ≠ 0, then the value of 2x² – 1 is :

(1) cos(\(\frac{4a}{\pi}\))

(2) sin(\(\frac{2a}{\pi}\))

(3) cos(\(\frac{2a}{\pi}\))

(4) sin(\(\frac{4a}{\pi}\))

Answer 1

Option : (2). sin(\(\frac{2a}{\pi}\))

Given,

a = (sin^-1x)²-(cos^-1x)²