Question

(cosx- cos y)^2 + (sinx - sin y)^2 = 4 sin^2(x-y/2)​

Answer 1

Answer:

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Answer 2

(cosx-cosy)^2 + (sinx-siny)^2 = 4sin^2(x-y/2)

LHS=(cosx-cosy)^2+(sinx-siny)^2

=cos^2x + cos^2y - 2cosxcosy + sin^2 +

sin^2y - 2sinxsiny

= (cos^2x + sin^2x) + (cos^2 + sin^2y) - 2(cosxcosy + sinxsiny) = 1+1-2cos (x-y)

= 2(1-cos(x-y) ) =4sin^2 x-y/2 = RHS

.

( . . 1- cos2x = 2sin^2 X )

hence proved......

I hope its helpful........