Question

How do you find all solutions if 0 ≤ θ < 2π for `tan 2theta = sqrt3`?

Answer 1

General solution is `(npi+pi/6)`, where `n` is an integer.

Explanation:

Note that `tan2theta=sqrt3`. As it is positive, it can lie either in 1st or 3rd quadrant. As `tan(pi/3)=sqrt3`, `2theta=pi/3` or `theta=pi/6`. In 3rd quadrant it will be `pi+pi/6`.

We can also have solutions by adding / subtracting `2pi` to these solutions.

Hence, general solution is `(npi+pi/6)`, where `n` is an integer.