a)

Square both sides:

Use the Pythagorean identity on the RHS:

Move everything to the LHS and you'll have a quadratic on cos x. Solve for cos x, and then find x. Can you take it from here?

b)

Solve for cos 3x:

Now ask yourself, the cosine of what angle(s) is 1/2? (You should know; they are all special angles!) The answers you come up with equal to3x, which means that you'll have to divide each of the answers by 3 to solve for x.