# Please, can anyone help me with this help to solve this question?. Verify that each x-value is a solution of the equation. 3 tan^2(5x) − 1 = 0. (a) x = pi/30 (b) x =5pi/30

## Please help to solve this question. Verify that each x-value is a solution of the equation. 3 tan^2(5x) − 1 = 0. (a) x = pi/30 (b) x =5pi/30

##### 1 Answer
Jun 12, 2018

$x = \frac{\pi}{30} + \frac{k \pi}{5}$
$x = \frac{5 \pi}{30} + \frac{k \pi}{5}$

#### Explanation:

$3 {\tan}^{2} \left(5 x\right) = 1$
${\tan}^{2} \left(5 x\right) = \frac{1}{3}$
$\tan \left(5\right) x = \pm \frac{\sqrt{3}}{3}$
a. tan (5x) = sqrt3/3
Trig table and unit circle give:
$5 x = \frac{\pi}{6} + k \pi$
$x = \frac{\pi}{30} + \frac{k \pi}{5}$
b. $\tan \left(5 x\right) = - \frac{\sqrt{3}}{3}$
$5 x = \frac{5 \pi}{6} + k \pi$
$x = \frac{5 \pi}{30} + \frac{k \pi}{5}$
Verification
$x = \frac{\pi}{30}$ --> $5 x = \frac{\pi}{6}$ -->
$3 {\tan}^{2} \left(\frac{\pi}{6}\right) = 3 {\left(\frac{1}{\sqrt{3}}\right)}^{2} = 1$. Proved
$x = \frac{5 \pi}{30} = \frac{\pi}{6}$--> $5 x = \frac{5 \pi}{6}$ -->
$3 {\tan}^{2} \left(5 \frac{\pi}{6}\right) = 3 {\left(\frac{1}{\sqrt{3}}\right)}^{2} = 1$. Proved