1.

Prove that (cos x + cos y)2 + (sin x – sin y)= 4cos2((x + y)/2)

Answer»

LHS = cos2x + cos2y + 2cosx cosy + sin2x + sin2y – 2sinxsin y 

= 1 + 1 + 2 (cosxcosy – sinxsiny) = 2[1 + cos (x + y)] = 4cos2((x + y)/2)



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