Answer :

We are given with,


We need to find the value of

Take Left Hand Side (LHS) of equation (i),

Using the property of inverse trigonometry,

Putting and ,

Equate LHS to RHS.

Taking cosine on both sides,

Using property of inverse trigonometry,

cos(cos-1 A) = A

Simplifying the equation,

Squaring on both sides,

Using algebraic identity,

(A – B)2 = A2 + B2 – 2AB

Using trigonometric identity,

cos 2θ = cos2 θ – sin2 θ …(ii)

sin2 θ + cos2 θ = 1 sin2 θ = 1 – cos2 θ …(iii)

Putting value of sin2 θ from equation (iii) in equation (ii), we get

cos 2θ = cos2 θ – (1 – cos2 θ)

Or, cos 2θ = cos2 θ – 1 + cos2 θ

Or, cos 2θ = 2 cos2 θ – 1

Or, 2 cos2 θ = cos 2θ + 1

Replace θ by θ/2.

Substituting the value of in

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