# Solve (sinx)(tanx) = 3sinx for 0 < x < 2pi. Round your answers to the nearest hundredth of a radian ?

May 10, 2018

$x = 3.14 , x = 1.25 \mathmr{and} x = 4.39$

#### Explanation:

Here,

$\sin x \tan x = 3 \sin x , w h e r e , 0 < x < 2 \pi$

$\implies \sin x \tan x - 3 \sin x = 0$

$\implies \sin x \left(\tan x - 3\right) = 0$

$\implies \sin x = 0 \mathmr{and} \tan x - 3 = 0$

$\sin x = 0 \mathmr{and} \tan x = 3$

$\left(1\right) \sin x = 0 , w h e r e , 0 < x < 2 \pi$

So, color(red)(x=pi=3.14^R

$\left(2\right) \tan x = 3 > 0 \implies {I}^{s t} Q u a \mathrm{dr} a n t \mathmr{and} I I {I}^{r d} Q u a \mathrm{dr} a n t$

$\left(i\right) {I}^{s t} Q u a \mathrm{dr} a n t \implies 0 < x \le \frac{\pi}{2}$

=>color(blue)(x=tan^-1(3)=1.25^R=(71.57)^circ

$\left(i i\right) I I {I}^{r d} Q u a \mathrm{dr} a n t \implies \pi \le x \le \frac{3 \pi}{2}$

=>color(blue)(x=pi+tan^-1 (3)=4.39^R=(251.57)^circ