Question

verify cos(a+b)cos(a-b)=cos^2b-sin^2a

Answer 1

try distributive property first then see what you get

Answer 2

so i got cos^2a-cos^2b

Answer 3

doing the left hand side

Answer 4

so now what?

Answer 5

how did you get that for the left hand side?

Answer 6

what is cos(a+b)?
what is cos(a-b)?
use the sum and difference identities for cosine.

Answer 7

I will tell you some hints.
You will need to multiply those. Since you will have something like (c-d)(c+d) remember all you need to do is c^2-d^2.
You will need to add in a zero to get what you want. Then do some factoring and recall that cos^2(x)+sin^2(x)=1. You will use this identity twice after using that zero.