If cos theta + cos 2theta + cos 3theta = 0,th | vedclass

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

Question

(D) Given the equation: $\cos 	heta + \cos 2	heta + \cos 3	heta = 0$ Grouping the terms: $(\cos 3	heta + \cos 	heta) + \cos 2	heta = 0$ Using th

Vedclass · Accepted Answer

Both $(A)$ and $(B)$

Vedclass · Answer

(D) Given the equation: $\cos 	heta + \cos 2	heta + \cos 3	heta = 0$ Grouping the terms: $(\cos 3	heta + \cos 	heta) + \cos 2	heta = 0$ Using the formula $\cos C + \cos D = 2 \cos \frac{C+D}{2} \cos \frac{C-D}{2}$: $2 \cos 2	heta \cos 	heta + \cos 2	heta = 0$ Factoring out $\cos 2	heta$: $\cos 2	heta (2 \cos 	heta + 1) = 0$ Case $1$: $\cos 2	heta = 0$ $2	heta = n\pi + \frac{\pi}{2}$ $	heta = \frac{n\pi}{2} + \frac{\pi}{4}$ Case $2$: $2 \cos 	heta + 1 = 0$ $\cos 	heta = -\frac{1}{2} = \cos \frac{2\pi}{3}$ $	heta = 2m\pi \pm \frac{2\pi}{3}$ Comparing with the options,the general solutions derived are $	heta = 2m\pi \pm \frac{2\pi}{3}$ and $	heta = \frac{n\pi}{2} + \frac{\pi}{4}$. Since the options provided are specific,we identify that $(A)$ and $(B)$ are valid subsets of the general solution set.

If $\cos \theta + \cos 2\theta + \cos 3\theta = 0$,then the general value of $\theta$ is

Similar Questions

If $\alpha$,$-\frac{\pi}{2} < \alpha < \frac{\pi}{2}$ is the solution of $4 \cos \theta + 5 \sin \theta = 1$,then the value of $\tan \alpha$ is

If $\frac{1 - \cos 2\theta}{1 + \cos 2\theta} = 3$,then the general value of $\theta$ is

The number of solutions of the equation $\sin A - 5 \sin 2A + \sin 3A = \cos A - 5 \cos 2A + \cos 3A$ in the interval $(0, \pi)$ is:

The number of roots of the equation $\cos^2 x + \frac{\sqrt{3} + 1}{2} \sin x - \frac{\sqrt{3}}{4} - 1 = 0$ that lie in the interval $[-\pi, \pi]$ is:

The number of values of $x$ in the interval $\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)$ for which $14 \operatorname{cosec}^{2} x - 2 \sin^{2} x = 21 - 4 \cos^{2} x$ holds,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module