Find all solutions

Question

Find all solutions to tanx= sin(2x) in the interval [0,2pi]. Then write a formula for the general solution (use k as your integer variable). Hint: apply a trig identity to one side of the equation, then simplify.

Answer 1

First, use the identity sin(2x) = 2sinxcosx.

You need to break into cases:

1. sinx equal 0
2. sinx not equal zero.

This should give you enough to do the rest. There are six solutions in [0,2pi].