tan x + sec x = sqrt 3

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- Apr 23rd 2014, 03:05 PMjennifernghisolve this trig equation. HELP!
tan x + sec x = sqrt 3

- Apr 23rd 2014, 04:16 PMtopsquarkRe: solve this trig equation. HELP!
- Apr 23rd 2014, 06:59 PMProve ItRe: solve this trig equation. HELP!
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.