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

Question

2322 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-04T01:12:12

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

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

$L H S = cos (3 x + 3 y) + cos (3 x - 3 y)$ $LHS=cos(3x + 3y) + cos(3x − 3y)$

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

$=2cos3xcos3y=RHS$

Proved

Prove the identity of cos(3x + 3y) + cos(3x − 3y) = 2 cos 3x cos 3ycos(3x+3y)+cos(3x−3y)=2cos3xcos3ycos(3x + 3y) + cos(3x − 3y) = 2 cos 3x cos 3y?