Question

prove that cos ( π/4- x) cos(π/4-y) - sin (π/4-x) sin(π/4-y) = sin(x+y)
pls follow me guys​

Answer 1

welcome to the concept of trignometry.

formula used ;

$\cos(x + y) = \cos(x) \cos(y) - \sin(x) \sin(y)$

then first solve LHS then problem become easy...

I hope my answer help you ✌️✌️.

mark answer as brainlist ❤️

Answer 2

Answer:

Lhs=1/2(2cos(pi/4-x)cos(pi/4-y))

- 1/2(2sin(pi/4-x)sin(pi/4-y))

=1/2(cos(pi/2-(x+y))+cos(x-y))

- 1/2(cos(x-y)-cos(pi/2-(x+y))

=1/2(sin(x+y)+cos(x-y))

- 1/2(cos(x-y)-sin(x+y))

=sin(x+y)