Problem

Find all solutions to the following equation:

Solution

Since there are a lot of terms involving trigonometric functions in this equation, we may first want to see if there any trig identities involving terms in our equation, so we can simplify things.

Since

we can put these two terms on the same side of the equation to get

In the interval [0, 2p], we have two solutions,

Since sin(x + 2p) = sin(x), the complete set of solutions to the above equation is

for any integer n

for any integer m