Q. 13

# Choose the correc

We are given with,

…(i)

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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