Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Solve the Following Equation: 2 Sin 2 X + √ 3 Cos X + 1 = 0 - Mathematics

Sum

Solve the following equation:

$2 \sin^2 x + \sqrt{3} \cos x + 1 = 0$

#### Solution

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

⇒ $(2 \cos x + \sqrt{3}) = 0$ or

$(\cos x - \sqrt{3}) = 0$
$\cos x = \sqrt{3}$ is not possible.

$\therefore 2 \cos x + \sqrt{3} = 0$
$\Rightarrow \cos x = - \frac{\sqrt{3}}{2}$
$\Rightarrow \cos x = \cos \frac{5\pi}{6}$
$\Rightarrow x = 2n\pi \pm \frac{5\pi}{6}, n \in$
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 3.3 | Page 22