Number of solutions of the equation cos theta | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given equation: $\cos 	heta + \cos 2	heta - \sqrt{3}(\sin 	heta + \sin 2	heta) + 1 = 0$. Using $\cos 2	heta = 2\cos^2 	heta - 1$ and $\sin 2

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Given equation: $\cos 	heta + \cos 2	heta - \sqrt{3}(\sin 	heta + \sin 2	heta) + 1 = 0$. Using $\cos 2	heta = 2\cos^2 	heta - 1$ and $\sin 2	heta = 2\sin 	heta \cos 	heta$: $\cos 	heta + 2\cos^2 	heta - 1 - \sqrt{3}\sin 	heta - 2\sqrt{3}\sin 	heta \cos 	heta + 1 = 0$. $\cos 	heta(1 + 2\cos 	heta) - \sqrt{3}\sin 	heta(1 + 2\cos 	heta) = 0$. $(1 + 2\cos 	heta)(\cos 	heta - \sqrt{3}\sin 	heta) = 0$. Case $1$: $1 + 2\cos 	heta = 0 \implies \cos 	heta = -1/2$. In $(0, 2\pi)$,$	heta = 2\pi/3, 4\pi/3$. Case $2$: $\cos 	heta - \sqrt{3}\sin 	heta = 0 \implies 	an 	heta = 1/\sqrt{3}$. In $(0, 2\pi)$,$	heta = \pi/6, 7\pi/6$. The solutions are $\pi/6, 2\pi/3, 7\pi/6, 4\pi/3$. Total number of solutions is $4$.

Number of solutions of the equation $\cos \theta + \cos 2\theta - \sqrt{3}(\sin \theta + \sin 2\theta) + 1 = 0$ lying in the interval $(0, 2\pi)$ is

Similar Questions

The principal solutions of $\cos 2x = -\frac{1}{2}$ are

If $\sin(2x) = \frac{\sqrt{5}-1}{4}$,then $x = \frac{n\pi}{2} + (-1)^n(m)$,where $n \in \mathbb{Z}$. Find $m$.

The smallest positive value of $x$ in degrees satisfying the equation $\tan(x+100^{\circ}) = \tan(x+50^{\circ}) \tan(x) \tan(x-50^{\circ})$ is (in $^{\circ}$)

The general solution of $\cot \frac{x}{2} - \cot x = \operatorname{cosec} \frac{x}{2}$ is

If $\cos \theta \neq 0$,and $\sec \theta - 1 = (\sqrt{2} - 1) \tan \theta$,then $\theta =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module