Q. 215.0( 4 Votes )

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Answer :

Given: To Prove: a sin 2θ + b cos 2θ = b

Given: We know that, By Pythagoras Theorem,

(Perpendicular)2 + (Base)2 = (Hypotenuse)2

(a)2 + (b)2 = (H)2

a2 + b2 = (H)2 So,  Taking LHS,

= a sin 2θ + b cos 2θ

We know that,

sin 2θ = 2 sin θ cos θ

and cos 2θ = 1 – 2 sin2θ

= a(2 sin θ cos θ) + b(1 – 2 sin2θ)

Putting the values of sinθ and cosθ, we get   = b

= RHS

LHS = RHS

Hence Proved

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