Question

prove that cos( pi/4-x) cos (pi/4 -y)- sin (pi/4 -x) sin (pi/4- y) = sin (x + y,)

Answer 1

$\cos(a) \cos(b) - \sin(a) \sin(b) = \cos(a + b)$
From the above eqn.,
Cos(pi/4 - x) cos(pi/4 - y) - sin(pi/4 - x) sin(pi/4 - y) = cos(pi/4 - x + pi/4 - y).
=cos(pi/2 - x + y).
$\cos( \frac{\pi}{2} - a ) = \sin(a)$
=sin(x+y).