The number of solutions of cos 2 theta = sin | vedclass

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

Question

(A) Given equation: $\cos 2 	heta = \sin 	heta$ Using the identity $\cos 2 	heta = 1 - 2 \sin^2 	heta$,we get: $1 - 2 \sin^2 	heta = \sin 	heta$

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) Given equation: $\cos 2 	heta = \sin 	heta$ Using the identity $\cos 2 	heta = 1 - 2 \sin^2 	heta$,we get: $1 - 2 \sin^2 	heta = \sin 	heta$ $2 \sin^2 	heta + \sin 	heta - 1 = 0$ Factoring the quadratic equation: $(2 \sin 	heta - 1)(\sin 	heta + 1) = 0$ This gives $\sin 	heta = \frac{1}{2}$ or $\sin 	heta = -1$. For $\sin 	heta = \frac{1}{2}$ in $(0, 2 \pi)$,$	heta = \frac{\pi}{6}$ and $	heta = \frac{5 \pi}{6}$. For $\sin 	heta = -1$ in $(0, 2 \pi)$,$	heta = \frac{3 \pi}{2}$. Thus,the solutions are $\frac{\pi}{6}, \frac{5 \pi}{6}, \frac{3 \pi}{2}$. The total number of solutions is $3$.

The number of solutions of $\cos 2 \theta = \sin \theta$ in the interval $(0, 2 \pi)$ is:

Similar Questions

The number of distinct solutions of the equation $\log _{\frac{1}{2}}|\sin x|=2-\log _{\frac{1}{2}}|\cos x|$ in the interval $[0,2 \pi]$ is

If $5\cos 2\theta + 2\cos^2\frac{\theta}{2} + 1 = 0$ and $-\pi < \theta < \pi$,then $\theta = $

When $a$ is irrational,the number of solutions satisfying the equation $1+\sin^2(ax)=\cos(x)$ 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 $\sum_{r=1}^{5} \cos(rx) = 0$ lying in the interval $(0, \pi)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module