If sin - 1 x 2 - cos - 1 x 2 = a ; 0 < x < 1 , a ≠ 0 , then the value of 2 x 2 - 1 is

Step-by-step solution

sin - 1 x 2 - cos - 1 x 2 = a Let sin - 1 x = t x = sin   t sin - 1 sin   t 2 - cos - 1 sin   t 2 = a t 2 - π 2 - t 2 = a t 2 - π 2 4 + t 2 - π t = a π t - π 2 4 = a t = a π + π 4 x = sin a π + π 4 2 x 2 - 1 = 2 sin 2 a π + π 4 - 1 = 2 sin a π   cos π 4 + cos a π   sin π 4 2 - 1 = sin a π + cos a π 2 - 1 = sin 2 a π + cos 2 a π + 2 cos a π sin a π - 1 = 2 cos a π sin a π = sin