sin (sin^-1 1/5 + cos^-1 x) = 1. Find x

Question

sin (sin^-1\(\frac 15\) + cos^-1 x) = 1. Find x

Answer 1

(using cos(A - B) = cos A cos B + sin A sin B)

⇒ x = ±\(\frac 15\)

(The value of sin(nπ + \(\frac{\pi}2\)) switches between 1 and -1)