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 solutions of $\tan x + \sec x = 2 \cos x$ in $[0, 2 \pi]$ are

If $n$ is any integer,then the general solution of the equation $\cos x - \sin x = \frac{1}{\sqrt{2}}$ is

Solve $\tan(x) + \sec(x) = \sqrt{3}$ for $x \in [0, 2\pi]$.

One of the solutions of the equation $8 \sin^3 \theta - 7 \sin \theta + \sqrt{3} \cos \theta = 0$ lies in the interval

If $\sin \theta = \sin \alpha$,then $\sin \frac{\theta}{3}$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module