Prove that -

(cos x + cos y)2 + (sin x - sin y)2 = 4 cos2[(x + y)/2]

We know that-




L.H.S = (cos x + cos y)2 + (sin x - sin y)2





= 4 cos2[(x + y)/2]×1 [∵ sin2x + cos2x = 1]


= 4 cos2[(x + y)/2]


= R.H.S


Hence, L.H.S = R.H.S…Proved


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