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