Question

Cos(5x)cos(2x) + sin(5x)(sin(2x)

Answer 1

Given: $cos(5x)cos(2x)+sin(5x)sin(2x)$

Recollect the following:

$cos(A-B)=cosAcosB+sinAsinB$

Using the above, we have

$cos(5x)cos(2x)+sin(5x)sin(2x)=cosAcosB+sinAsinB, A=5x,B=2x$

$=cos(A-B)$

$=cos(5x-2x)$

$=cos(3x)$

Therefore, $cos(5x)cos(2x)+sin(5x)sin(2x)=cos(3x)$