cos frac{pi}{2^2} cdot cos frac{pi}{2^3} cdot | vedclass

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Question

(A) माना $P = \cos \frac{\pi}{2^2} \cdot \cos \frac{\pi}{2^3} \cdot \dots \cdot \cos \frac{\pi}{2^{10}}$.सर्वसमिका $\cos 	heta \cdot \cos 2	heta \cd

Vedclass · Accepted Answer

$\frac{1}{512}$

Vedclass · Answer

(A) माना $P = \cos \frac{\pi}{2^2} \cdot \cos \frac{\pi}{2^3} \cdot \dots \cdot \cos \frac{\pi}{2^{10}}$.सर्वसमिका $\cos 	heta \cdot \cos 2	heta \cdot \cos 4	heta \dots \cos 2^{n-1}	heta = \frac{\sin(2^n 	heta)}{2^n \sin 	heta}$ का उपयोग करते हुए,$	heta = \frac{\pi}{2^{10}}$ और $n = 9$ रखने पर.अतः $P = \frac{\sin(2^9 \cdot \frac{\pi}{2^{10}})}{2^9 \sin(\frac{\pi}{2^{10}})} = \frac{\sin(\frac{\pi}{2})}{512 \sin(\frac{\pi}{2^{10}})} = \frac{1}{512 \sin(\frac{\pi}{2^{10}})}$.दिया गया व्यंजक $P \cdot \sin \frac{\pi}{2^{10}} = \frac{1}{512 \sin(\frac{\pi}{2^{10}})} \cdot \sin \frac{\pi}{2^{10}} = \frac{1}{512}$ है।

$\cos \frac{\pi}{2^2} \cdot \cos \frac{\pi}{2^3} \cdot \dots \cdot \cos \frac{\pi}{2^{10}} \cdot \sin \frac{\pi}{2^{10}}$ का मान है

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