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Question

cos{π/4 - x}cos{π/4 - y} - sin{π/4 - x}sin{π/4 - y} = sin(x+y)

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Solution

Using formula: cosA.cosB-sinA.sinB=cos(A+B)

cos(π/4 - x) cos(π/4 - y) - sin(π/4 - x)sin(π/4 - y)
=cos{(π/4 - x)+(π/4 - y)}
=cos{π/4 - x+π/4 - y}
=cos{π/2 - x - y}
=cos{π/2 -( x + y)}
=sin( x + y) hence proved

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