Prove that : cos 2x cos 2 y + sin^2 (x - y) - sin^2 (x + y) = cos (2x + 2y).
Answers
Answered by
5
Answer:
Step-by-step explanation:
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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Answered by
0
Answer:
Sin2x-sin2y/cos2y-cos2x
={2cos(2x+2y)/2sin(2x-2y)/2}/{2sin(2y+2x)/2sin(2x-2y)/2}
[∵, sinC-sinD=2cos(C+D)/2sin(C-D)/2 and cosC-cosD=2sin(C+D)/2sin(D-C)/2]
=cos(x+y)sin(x-y)/sin(x+y)sin(x-y)
=cot(x+y) (Proved
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