a)
b)
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 to 3x, which means that you'll have to divide each of the answers by 3 to solve for x.
Eumyang is right, although this method does lead to an extraneous answer, so you have to be careful: we have:
However, this would lead to one set of solutions which actually doesn't fit the original equation. The problem arises from the fact that, given the equations
we have (1) implies (2), but not (2) implies (1).