The value of sin frac{pi}{16} sin frac{3pi}{1 | vedclass

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

Question

(B) Let $S = \sin \frac{\pi}{16} \sin \frac{3\pi}{16} \sin \frac{5\pi}{16} \sin \frac{7\pi}{16}$.Using $\sin 	heta = \cos(\frac{\pi}{2} - 	heta)$,we

Vedclass · Accepted Answer

$\frac{\sqrt{2}}{16}$

Vedclass · Answer

(B) Let $S = \sin \frac{\pi}{16} \sin \frac{3\pi}{16} \sin \frac{5\pi}{16} \sin \frac{7\pi}{16}$.Using $\sin 	heta = \cos(\frac{\pi}{2} - 	heta)$,we have $\sin \frac{7\pi}{16} = \cos \frac{\pi}{16}$ and $\sin \frac{5\pi}{16} = \cos \frac{3\pi}{16}$.So,$S = (\sin \frac{\pi}{16} \cos \frac{\pi}{16}) (\sin \frac{3\pi}{16} \cos \frac{3\pi}{16})$.Using $2 \sin 	heta \cos 	heta = \sin 2	heta$,we get $S = (\frac{1}{2} \sin \frac{\pi}{8}) (\frac{1}{2} \sin \frac{3\pi}{8}) = \frac{1}{4} \sin \frac{\pi}{8} \cos \frac{\pi}{8}$ (since $\sin \frac{3\pi}{8} = \cos \frac{\pi}{8}$).$S = \frac{1}{8} \sin \frac{\pi}{4} = \frac{1}{8} 	imes \frac{1}{\sqrt{2}} = \frac{1}{8\sqrt{2}} = \frac{\sqrt{2}}{16}$.

The value of $\sin \frac{\pi}{16} \sin \frac{3\pi}{16} \sin \frac{5\pi}{16} \sin \frac{7\pi}{16}$ is

Similar Questions

If $|\sin x-\cos ^2 x| \geq|3-3 \sin x+\sin ^2 x|+4|\sin x-1|$,then $x=$

If $\sin \theta \cosh \alpha = \tan x$ and $\cos \theta \sinh \alpha = \sec x$,then find the value of $\cos 2 \theta \cosh 2 \alpha$.

If $r \sin \theta = 3$ and $r = 4(1 + \sin \theta)$ for $0 \le \theta \le 2\pi$,then $\theta = $

The number of solutions of the equation $2 \cos(e^x) = 5^x + 5^{-x}$ is:

The value of $\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} + \cos^2 \frac{5\pi}{12}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module