First slide

Trigonometric equations

Question

The solution set of the equation $4 \sin θ . \cos θ - 2 \cos θ - 2 \sqrt{3} \sin θ + \sqrt{3} = 0$ in the interval $(0, 2 π)$ is

Easy

A

${\frac{3 π}{4}, \frac{7 π}{4}}$
B

${\frac{π}{3}, \frac{5 π}{3}}$
C

${\frac{3 π}{4}, π, \frac{π}{3}, \frac{5 π}{3}}$
D

${\frac{π}{6}, \frac{5 π}{6}, \frac{11 π}{6}}$

Solution

$4 \sin θ . \cos θ - 2 \cos θ - 2 \sqrt{3} \sin θ + \sqrt{3} = 0$
$\Rightarrow 2 \cos θ (2 \sin θ - 1) - \sqrt{3} (2 \sin θ - 1) = 0$

$\Rightarrow (2 \sin θ - 1) (2 \cos θ - \sqrt{3}) = 0$

$\Rightarrow \sin θ = \frac{1}{2}, \frac{\sqrt{3}}{2} \Rightarrow θ = \frac{π}{6}, \frac{5 π}{6}, \frac{11 π}{6}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App