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 A cos B - sin A sinB

= cos(A+B)

given expression

$= \cos( \frac{\pi}{4} - x + \frac{\pi}{4} - y )$
$= \cos( \frac{\pi}{2} - (x + y) )$
$= \sin(x + y)$