यदि frac{cos^4 alpha}{cos^2 beta} + frac{sin^ | vedclass

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(B) दिया गया है: $\frac{\cos^4 \alpha}{\cos^2 \beta} + \frac{\sin^4 \alpha}{\sin^2 \beta} = 1$.मान लीजिए $\frac{\cos^2 \alpha}{\cos \beta} = \cos 	he

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) दिया गया है: $\frac{\cos^4 \alpha}{\cos^2 \beta} + \frac{\sin^4 \alpha}{\sin^2 \beta} = 1$.मान लीजिए $\frac{\cos^2 \alpha}{\cos \beta} = \cos 	heta$ और $\frac{\sin^2 \alpha}{\sin \beta} = \sin 	heta$.तब $\cos^2 \alpha = \cos \beta \cos 	heta$ और $\sin^2 \alpha = \sin \beta \sin 	heta$.इनका योग करने पर,$\cos^2 \alpha + \sin^2 \alpha = \cos \beta \cos 	heta + \sin \beta \sin 	heta = \cos(\beta - 	heta) = 1$.इसका अर्थ है $\beta = 	heta + 2n\pi$,अतः $\cos \beta = \cos 	heta$ और $\sin \beta = \sin 	heta$.मान प्रतिस्थापित करने पर,$\cos^2 \alpha = \cos^2 \beta$ और $\sin^2 \alpha = \sin^2 \beta$.अतः,$\frac{\cos^4 \beta}{\cos^2 \alpha} + \frac{\sin^4 \beta}{\sin^2 \alpha} = \frac{\cos^4 \beta}{\cos^2 \beta} + \frac{\sin^4 \beta}{\sin^2 \beta} = \cos^2 \beta + \sin^2 \beta = 1$.$1$ का महत्तम पूर्णांक $[1] = 1$ है।

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