To find: value of x

Given:

LHS = cos(sin^-1 x) … (1)

Let sin θ = x

Therefore θ = sin^-1 x … (2)

From the figure,

… (3)

From (2) and (3),

… (4)

Substituting (4) in (1), we get

LHS

Therefore,

Squaring and simplifying,

⇒ 81 – 81x² = 1

⇒ 81x² = 80

Therefore, are the required values of x.