The value of sin ^2 frac{pi}{8} + sin ^2 frac | vedclass

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

Question

(B) We know that $\sin(\pi - 	heta) = \sin 	heta$.$\sin \frac{7\pi}{8} = \sin(\pi - \frac{\pi}{8}) = \sin \frac{\pi}{8}$$\sin \frac{5\pi}{8} = \sin(

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) We know that $\sin(\pi - 	heta) = \sin 	heta$.$\sin \frac{7\pi}{8} = \sin(\pi - \frac{\pi}{8}) = \sin \frac{\pi}{8}$$\sin \frac{5\pi}{8} = \sin(\pi - \frac{3\pi}{8}) = \sin \frac{3\pi}{8}$Substituting these into the expression:$	ext{Expression} = \sin ^2 \frac{\pi}{8} + \sin ^2 \frac{3\pi}{8} + \sin ^2 \frac{3\pi}{8} + \sin ^2 \frac{\pi}{8}$$= 2(\sin ^2 \frac{\pi}{8} + \sin ^2 \frac{3\pi}{8})$Since $\sin \frac{3\pi}{8} = \sin(\frac{\pi}{2} - \frac{\pi}{8}) = \cos \frac{\pi}{8}$,we have:$= 2(\sin ^2 \frac{\pi}{8} + \cos ^2 \frac{\pi}{8})$Using the identity $\sin ^2 	heta + \cos ^2 	heta = 1$:$= 2(1) = 2$

The value of $\sin ^2 \frac{\pi}{8} + \sin ^2 \frac{3\pi}{8} + \sin ^2 \frac{5\pi}{8} + \sin ^2 \frac{7\pi}{8}$ is

Similar Questions

$\cos 36^{\circ} - \cos 72^{\circ}$ is equal to

$\cos ^2\left(\frac{7 \pi}{8}\right)+\cos ^2\left(\frac{5 \pi}{8}\right)+\cos ^2\left(\frac{3 \pi}{8}\right)+\cos ^2\left(\frac{\pi}{8}\right)=$

The value of $\tan (-945^\circ)$ is

The degree measure of $\frac{\pi}{32}$ radians is equal to:

Which of the following relations is possible?

Vedclass Test Series

Exam Paper Generator

Online Exam Module