Question

Prove that cos(π/4-x)cos(π/4-y) - sin(π/4-x)sin(π/4-y) = sin(x+y)

Answer 1

cos(π/4 - x) cos(π/4 - y) - sin(π/4 - x)sin(π/4 - y)

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)