The values of theta satisfying sin 7theta = s | vedclass

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

Question

(A) Given the equation: $\sin 7	heta = \sin 4	heta - \sin 	heta$Rearranging the terms: $\sin 7	heta + \sin 	heta = \sin 4	heta$Using the sum-to-

Vedclass · Accepted Answer

$\frac{\pi}{9}, \frac{\pi}{4}$

Vedclass · Answer

(A) Given the equation: $\sin 7	heta = \sin 4	heta - \sin 	heta$Rearranging the terms: $\sin 7	heta + \sin 	heta = \sin 4	heta$Using the sum-to-product formula $\sin C + \sin D = 2 \sin(\frac{C+D}{2}) \cos(\frac{C-D}{2})$:$2 \sin(\frac{7	heta + 	heta}{2}) \cos(\frac{7	heta - 	heta}{2}) = \sin 4	heta$$2 \sin 4	heta \cos 3	heta = \sin 4	heta$$2 \sin 4	heta \cos 3	heta - \sin 4	heta = 0$$\sin 4	heta (2 \cos 3	heta - 1) = 0$This gives two cases:Case $1$: $\sin 4	heta = 0$$4	heta = n\pi$,so $	heta = \frac{n\pi}{4}$. For $0 Case $2$: $2 \cos 3	heta - 1 = 0 \Rightarrow \cos 3	heta = \frac{1}{2}$$3	heta = 2n\pi \pm \frac{\pi}{3}$. For $0 Thus,the values are $\frac{\pi}{9}$ and $\frac{\pi}{4}$.

The values of $\theta$ satisfying $\sin 7\theta = \sin 4\theta - \sin \theta$ and $0 < \theta < \frac{\pi}{2}$ are

Similar Questions

The most general value of $\theta$ which satisfies both the equations $\tan \theta = -1$ and $\cos \theta = \frac{1}{\sqrt{2}}$ is

If $\sin 2\theta = \cos 3\theta$ and $\theta$ is an acute angle,then $\sin \theta$ is equal to

If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$

If the equation in variable $\theta$,$3 \tan(\theta - \alpha) = \tan(\theta + \alpha)$,(where $\alpha$ is a constant) has no real solution,then $\alpha$ can be (wherever $\tan(\theta - \alpha)$ and $\tan(\theta + \alpha)$ are both defined).

The sum of all values of $x$ in $[0, 2\pi]$,for which $\sin x + \sin 2x + \sin 3x + \sin 4x = 0$,is equal to: (in $\pi$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module