First slide

Trigonometric equations

Question

General solution of $\tan^{2} x + (1 - \sqrt{3}) \tan x - \sqrt{3} = 0$ is

Easy

A

$n π + \frac{π}{6}$
B

$n π + \frac{π}{4}$
C

$n π + \frac{π}{2}$
D

$n π + \frac{π}{3}, n π - \frac{π}{4}$

Solution

We have $\tan^{2} x + (1 - \sqrt{3}) \tan x - \sqrt{3} = 0$
$\Rightarrow \tan x = \sqrt{3} o r \tan x = - 1$
$\Rightarrow x = n π + \frac{π}{3} o r x = n π - \frac{π}{4}$

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