# Question #37b3d

Aug 18, 2016

$\pm \frac{\pi}{3} + 2 k \pi$

#### Explanation:

Simplify both sides by ${\cos}^{2} t$. (Condition cos x different to 0)
The remainder equation is:
$\frac{1}{{\cos}^{2} t} + 5 = 3 \frac{{\sin}^{2} t}{{\cos}^{2} t}$
$\frac{1 + 5 {\cos}^{2} t}{{\cos}^{2} t} = \frac{3 {\sin}^{2} t}{{\cos}^{2} t}$
Simplify both sides by ${\cos}^{2} t .$
Replace in the equation $3 {\sin}^{2} t$ by $\left(3 - 3 {\cos}^{2} t\right)$-->
$1 + 5 {\cos}^{2} t = 3 - 3 {\cos}^{2} t$
$8 {\cos}^{2} t = 2$ --> ${\cos}^{2} t = \frac{2}{8} = \frac{1}{4}$
$\cos t = \pm \frac{1}{2}$
Trig table and unit circle -->
$\cos t = \pm \frac{1}{2}$ --> $t = \pm \frac{\pi}{3}$
$t = \pm \frac{\pi}{3} + 2 k \pi$