Question

Express cos9x+cos5x as a product.

Can you just multiply the 9 and 5 to get: cos45x
? is that a product?

Answer 1

oohhhh noooo!

we have a formula
cosA + cosB = 2cos(A+B)/2 * cos(A-B)/2

so cos 9x + cos 5x = 2cos(9x+5x)/2 cos(9x-5x)/2
= 2(cos 7x)(cos 2x)