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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 – 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,