Question

How do you solve `sqrt(tanx)=root4(3)` in the interval [0,360]?

Answer 1

Rewrite both sides in radical form.

`(tanx)^(1/2) = 3^(1/4)`

We need to balance exponents.

`((tanx)^(1/2))^4 = (3^(1/4))^4`

`(tanx)^2 = 3`

`tan^2x = 3`

`tanx = +-sqrt(3)`

`x = 60^@, 120^@, 240^@, 300^@`

However, we can only take the solutions when the `sqrt(3)` is positive, since the solutions located in quadrants where tangent is negative will render the original equation undefined.

So, `x = 60^@ and 240^@`

Hopefully this helps!