If cos theta + cos 7theta + cos 3theta + cos | vedclass

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

Question

(C) Given equation: $\cos 	heta + \cos 7	heta + \cos 3	heta + \cos 5	heta = 0$Using the sum-to-product formula $\cos C + \cos D = 2 \cos \frac{C+D

Vedclass · Accepted Answer

$\frac{n\pi}{8}$

Vedclass · Answer

(C) Given equation: $\cos 	heta + \cos 7	heta + \cos 3	heta + \cos 5	heta = 0$Using the sum-to-product formula $\cos C + \cos D = 2 \cos \frac{C+D}{2} \cos \frac{C-D}{2}$:$(\cos 7	heta + \cos 	heta) + (\cos 5	heta + \cos 3	heta) = 0$$2 \cos 4	heta \cos 3	heta + 2 \cos 4	heta \cos 	heta = 0$$2 \cos 4	heta (\cos 3	heta + \cos 	heta) = 0$Using $\cos 3	heta + \cos 	heta = 2 \cos 2	heta \cos 	heta$:$2 \cos 4	heta (2 \cos 2	heta \cos 	heta) = 0$$4 \cos 4	heta \cos 2	heta \cos 	heta = 0$This implies $\cos 4	heta = 0$ or $\cos 2	heta = 0$ or $\cos 	heta = 0$.If $\cos 4	heta = 0$,then $4	heta = (2n+1)\frac{\pi}{2} \implies 	heta = (2n+1)\frac{\pi}{8}$.If $\cos 2	heta = 0$,then $2	heta = (2n+1)\frac{\pi}{2} \implies 	heta = (2n+1)\frac{\pi}{4}$.If $\cos 	heta = 0$,then $	heta = (2n+1)\frac{\pi}{2}$.Combining these,the general solution is $	heta = \frac{n\pi}{8}$.

If $\cos \theta + \cos 7\theta + \cos 3\theta + \cos 5\theta = 0$,then $\theta$ is equal to:

Similar Questions

If $0 < \theta < \frac{\pi}{2}$ and $\tan 3 \theta \neq 0$, then $\tan \theta + \tan 2 \theta + \tan 3 \theta = 0$ if $\tan \theta \cdot \tan 2 \theta = k$, where $k =$

Let $P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \}$ and $Q = \{ \theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \}$ be two sets. Then

$\frac{1+\cos \theta-\sin \theta}{1+\cos \theta+\sin \theta}+\frac{1+\cos \theta+\sin \theta}{1+\cos \theta-\sin \theta}=$

If $\tan \left(\frac{\pi}{4}+\alpha\right)=\tan ^3\left(\frac{\pi}{4}+\beta\right)$,then $\tan (\alpha+\beta) \cot (\alpha-\beta)=$

$\sin^6 \theta + \cos^6 \theta + 3 \sin^2 \theta \cos^2 \theta = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module