1.

Prove that cos2xcos2y+sin^2(x-y)-sin^2(x+y)= cos(2x+2y)

Answer»

ANSWER:

To prove: cos 2θ cos2φ + sin^2 (θ – φ) – sin^2(θ + φ) = cos (2θ + 2φ)

Proof:

LHS = cos 2θ cos2φ + SIN2 (θ – φ) – sin2(θ + φ)

= cos 2θ cos2φ + sin (θ – φ + θ + φ) sin(θ – φ - θ - φ) [Using: sin2 A - sin2 B = sin(A + B) sin (A - B)]

= cos 2θ cos2φ + sin 2θ sin(-2φ)

= cos 2θ cos2φ - sin 2θ sin 2φ

= cos (2θ + 2φ) [using: cos (A + B) = cos A cos B - sin A sin B]

= RHS [Hence PROVED]

Hope it will help you.



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