Choose the correct answer

If , then

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 – a^{2})√(1 – b^{2}))

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} = x^{2} + y^{2} – 2xy

Simplifying it further,

Shifting all terms at one side,

Using trigonometric identity,

sin^{2} x + cos^{2} x = 1

⇒ sin^{2} x = 1 – cos^{2} x

We get,

1