Question

Prove the identity of `cos(3x + 3y) + cos(3x − 3y) = 2 cos 3x cos 3y`?

Answer 1

using identities `cos(A+B)=cosAcosB-sinAsinB`

`cos(A-B)=cosAcosB+sinAsinB` weget

`LHS=cos(3x + 3y) + cos(3x − 3y)`

`=cos3xcos3y-cancel(sin3xsin3y)+cos3xcos3y+cancel(sin3xsin3y)`

`=2cos3xcos3y=RHS`

Proved