Here's a "cute" way to approach this problem . . .
. . we see that and are angles in the same right triangle . . .
Code:* * * * 3x * * * * * * * * 2x * * * * * * * * *
Of course, this is not a complete solution . . .
Pull everything to the LHS and factor the common cos(x):
So either or
For the sin solution, use the quadratic formula to find:
So the whole solution set in the domain will be x = from the solution and x = from the sine solution. These may be easily seen to be the same solutions as ThePerfectHacker gave you, only from a much messier derivation.