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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