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))


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,


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