Answer :

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))


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,

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