sin ^4 frac{pi}{8} + sin ^4 frac{3pi}{8} + si | vedclass

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

Question

(C) हम जानते हैं कि $\sin \frac{5\pi}{8} = \sin(\pi - \frac{3\pi}{8}) = \sin \frac{3\pi}{8}$ और $\sin \frac{7\pi}{8} = \sin(\pi - \frac{\pi}{8}) = \si

Vedclass · Accepted Answer

$\frac{3}{2}$

Vedclass · Answer

(C) हम जानते हैं कि $\sin \frac{5\pi}{8} = \sin(\pi - \frac{3\pi}{8}) = \sin \frac{3\pi}{8}$ और $\sin \frac{7\pi}{8} = \sin(\pi - \frac{\pi}{8}) = \sin \frac{\pi}{8}$ होता है।अतः,व्यंजक $2(\sin^4 \frac{\pi}{8} + \sin^4 \frac{3\pi}{8})$ बन जाता है।सर्वसमिका $\sin^2 	heta = \frac{1 - \cos 2	heta}{2}$ का उपयोग करते हुए,$\sin^4 	heta = (\frac{1 - \cos 2	heta}{2})^2 = \frac{1}{4}(1 - 2\cos 2	heta + \cos^2 2	heta) = \frac{1}{4}(1 - 2\cos 2	heta + \frac{1 + \cos 4	heta}{2}) = \frac{1}{8}(3 - 4\cos 2	heta + \cos 4	heta)$ प्राप्त होता है।$	heta = \frac{\pi}{8}$ के लिए: $\sin^4 \frac{\pi}{8} = \frac{1}{8}(3 - 4\cos \frac{\pi}{4} + \cos \frac{\pi}{2}) = \frac{1}{8}(3 - 4(\frac{1}{\sqrt{2}}) + 0) = \frac{3 - 2\sqrt{2}}{8}$।$	heta = \frac{3\pi}{8}$ के लिए: $\sin^4 \frac{3\pi}{8} = \frac{1}{8}(3 - 4\cos \frac{3\pi}{4} + \cos \frac{3\pi}{2}) = \frac{1}{8}(3 - 4(-\frac{1}{\sqrt{2}}) + 0) = \frac{3 + 2\sqrt{2}}{8}$।इनका योग करने पर: $2(\frac{3 - 2\sqrt{2}}{8} + \frac{3 + 2\sqrt{2}}{8}) = 2(\frac{6}{8}) = 2(\frac{3}{4}) = \frac{3}{2}$।

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

Similar Questions

$\frac{{\cos 12^\circ - \sin 12^\circ }}{{\cos 12^\circ + \sin 12^\circ }} + \frac{{\sin 147^\circ }}{{\cos 147^\circ }} = $

यदि $\sin \theta + \cos \theta = 1$ है,तो $\sin \theta \cos \theta = $

निम्नलिखित में से कौन सी संख्या/संख्याएँ परिमेय है/हैं?

$\cos^2 \left( \frac{\pi}{4} - \beta \right) - \sin^2 \left( \alpha - \frac{\pi}{4} \right) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module