sin ^4 frac{pi}{8}+sin ^4 frac{2 pi}{8}+sin ^ | vedclass

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

Question

(C) माना $S = \sum_{k=1}^{7} \sin^4 \frac{k\pi}{8}$.$\sin(\pi - 	heta) = \sin 	heta$ गुणधर्म का उपयोग करने पर,हमें प्राप्त होता है $\sin \frac{7\pi}

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) माना $S = \sum_{k=1}^{7} \sin^4 \frac{k\pi}{8}$.$\sin(\pi - 	heta) = \sin 	heta$ गुणधर्म का उपयोग करने पर,हमें प्राप्त होता है $\sin \frac{7\pi}{8} = \sin \frac{\pi}{8}$,$\sin \frac{6\pi}{8} = \sin \frac{2\pi}{8}$,और $\sin \frac{5\pi}{8} = \sin \frac{3\pi}{8}$.अतः,$S = 2(\sin^4 \frac{\pi}{8} + \sin^4 \frac{2\pi}{8} + \sin^4 \frac{3\pi}{8}) + \sin^4 \frac{4\pi}{8}$.चूँकि $\sin \frac{2\pi}{8} = \sin \frac{\pi}{4} = \frac{1}{\sqrt{2}}$ और $\sin \frac{4\pi}{8} = \sin \frac{\pi}{2} = 1$,इसलिए $\sin^4 \frac{2\pi}{8} = (\frac{1}{\sqrt{2}})^4 = \frac{1}{4}$ और $\sin^4 \frac{4\pi}{8} = 1^4 = 1$ है।अब,$\sin^4 \frac{\pi}{8} + \sin^4 \frac{3\pi}{8} = \sin^4 \frac{\pi}{8} + \cos^4 \frac{\pi}{8} = (\sin^2 \frac{\pi}{8} + \cos^2 \frac{\pi}{8})^2 - 2\sin^2 \frac{\pi}{8} \cos^2 \frac{\pi}{8} = 1 - \frac{1}{2}\sin^2 \frac{\pi}{4} = 1 - \frac{1}{2}(\frac{1}{2}) = 1 - \frac{1}{4} = \frac{3}{4}$.इन मानों को व्यंजक में रखने पर:$S = 2(\frac{3}{4} + \frac{1}{4}) + 1 = 2(1) + 1 = 3$.

$\sin ^4 \frac{\pi}{8}+\sin ^4 \frac{2 \pi}{8}+\sin ^4 \frac{3 \pi}{8}+\sin ^4 \frac{4 \pi}{8}+\sin ^4 \frac{5 \pi}{8}+\sin ^4 \frac{6 \pi}{8}+\sin ^4 \frac{7 \pi}{8} = ?$

Similar Questions

$4 \cos \frac{7 \theta}{2} \cos \frac{3 \theta}{2} \sin 5 \theta = $

यदि $\cos(\theta - \alpha) = a$ और $\sin(\theta - \beta) = b$ है,तो $\cos^2(\alpha - \beta) + 2ab\sin(\alpha - \beta)$ का मान क्या होगा?

$\cos^2 10^o - \cos 10^o \cos 50^o + \cos^2 50^o$ का मान क्या है?

$\sum_{k=1}^3 \cos ^2\left((2 k-1) \frac{\pi}{12}\right)$ का मान ज्ञात कीजिए।

यदि $\pi < \alpha < \frac{3\pi}{2}$ है,तो $\sqrt{\frac{1 - \cos \alpha}{1 + \cos \alpha}} + \sqrt{\frac{1 + \cos \alpha}{1 - \cos \alpha}} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module