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Question
Prove the following: `cos (pi/4 xx x) cos (pi/4 - y) - sin (pi/4 - x)sin (pi/4 - y) = sin (x + y)`
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Solution
L.H.S. `cos (pi/4 xx x) cos (pi/4 - y) - sin (pi/4 - x)sin (pi/4 - y)`
= cos `[(pi/4 - x + pi/4 - y)]`
[∵ cos A cos B - sin A sin B = cos (A + B)]
= cos `(pi/2 - (x +y))`
= sin (x + y) = R.H.S. `(∵ cos (pi/2 - θ) = sin θ)`
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