The sum of all values of theta in (0, frac{pi | vedclass

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

Question

(C) Given equation: $\sin^2 2	heta + \cos^4 2	heta = \frac{3}{4}$.Using the identity $\sin^2 2	heta = 1 - \cos^2 2	heta$,we get:$1 - \cos^2 2	het

Vedclass · Accepted Answer

$\frac{\pi}{2}$

Vedclass · Answer

(C) Given equation: $\sin^2 2	heta + \cos^4 2	heta = \frac{3}{4}$.Using the identity $\sin^2 2	heta = 1 - \cos^2 2	heta$,we get:$1 - \cos^2 2	heta + \cos^4 2	heta = \frac{3}{4}$.Let $t = \cos^2 2	heta$. Then the equation becomes $t^2 - t + 1 = \frac{3}{4}$,which simplifies to $t^2 - t + \frac{1}{4} = 0$.This is $(t - \frac{1}{2})^2 = 0$,so $t = \frac{1}{2}$.Thus,$\cos^2 2	heta = \frac{1}{2}$,which implies $\cos 4	heta = 2\cos^2 2	heta - 1 = 2(\frac{1}{2}) - 1 = 0$.For $	heta \in (0, \frac{\pi}{2})$,$4	heta \in (0, 2\pi)$.$\cos 4	heta = 0$ implies $4	heta = \frac{\pi}{2}, \frac{3\pi}{2}$.Therefore,$	heta = \frac{\pi}{8}, \frac{3\pi}{8}$.The sum of these values is $\frac{\pi}{8} + \frac{3\pi}{8} = \frac{4\pi}{8} = \frac{\pi}{2}$.

The sum of all values of $\theta \in (0, \frac{\pi}{2})$ satisfying $\sin^2 2\theta + \cos^4 2\theta = \frac{3}{4}$ is

Similar Questions

If $\sin \alpha = \frac{336}{625}$ and $450^\circ < \alpha < 540^\circ$,then $\sin \left( \frac{\alpha}{4} \right) = $

The value of $\cos 12^\circ + \cos 84^\circ + \cos 156^\circ + \cos 132^\circ$ is

If $x = \operatorname{cosec} \theta - \sin \theta$ and $y = \sec \theta - \cos \theta$,then the relation between $x$ and $y$ is

$(\sec A + \tan A - 1)(\sec A - \tan A + 1) - 2\tan A = $

The value of $\log \tan 1^{\circ} + \log \tan 2^{\circ} + \log \tan 3^{\circ} + \ldots + \log \tan 89^{\circ}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module