We are given that,

We need to find the value of

By property of inverse trigonometry,

cos^-1 a + cos^-1 b = cos^-1(ab - √(1 – a²)√(1 – b²))

So,

Simplifying further,

Taking cosine on both sides,

Using the property of inverse trigonometric function,

cos(cos^-1 x) = x

To simplify it further, take square on both sides.

Using algebraic identity,

(x – y)² = x² + y² – 2xy

Simplifying it further,

Shifting all terms at one side,

Using trigonometric identity,

sin² x + cos² x = 1

⇒ sin² x = 1 – cos² x

We get,