# Thread: solve this trig equation. HELP!

1. ## solve this trig equation. HELP!

tan x + sec x = sqrt 3

2. ## Re: solve this trig equation. HELP!

Originally Posted by jennifernghi
tan x + sec x = sqrt 3
What have you tried so far?

-Dan

3. ## Re: solve this trig equation. HELP!

Originally Posted by jennifernghi
tan x + sec x = sqrt 3
As a start...

\displaystyle \begin{align*} \tan{(x)} + \sec{(x)} &= \sqrt{3} \\ \frac{\sin{(x)}}{\cos{(x)}} + \frac{1}{\cos{(x)}} &= \sqrt{3} \\ \frac{\sin{(x)} + 1}{\cos{(x)}} &= \sqrt{3} \\ \sin{(x)} + 1 &= \sqrt{3}\cos{(x)} \end{align*}

Now you need some way to convert everything to sines or cosines. Squaring and applying the Pythagorean Identity would work, you just need to be careful for extraneous solutions.