यदि cos (alpha + beta) = frac{3}{5},sin (alph | vedclass

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Question

(C) दिया गया है $0 < \alpha, \beta < \frac{\pi}{4}$,इसलिए $0 < \alpha + \beta < \frac{\pi}{2}$ और $-\frac{\pi}{4} < \alpha - \beta < \frac{\pi}{4}$ है

Vedclass · Accepted Answer

$\frac{63}{16}$

Vedclass · Answer

(C) दिया गया है $0 चूंकि $\cos(\alpha + \beta) = \frac{3}{5}$,इसलिए $	an(\alpha + \beta) = \frac{4}{3}$ है।चूंकि $\sin(\alpha - \beta) = \frac{5}{13}$,इसलिए $\cos(\alpha - \beta) = \sqrt{1 - (\frac{5}{13})^2} = \frac{12}{13}$ है,अतः $	an(\alpha - \beta) = \frac{5}{12}$ है।अब,$	an(2\alpha) = 	an((\alpha + \beta) + (\alpha - \beta))$ है।सूत्र $	an(A + B) = \frac{	an A + 	an B}{1 - 	an A 	an B}$ का उपयोग करने पर:$	an(2\alpha) = \frac{\frac{4}{3} + \frac{5}{12}}{1 - (\frac{4}{3} 	imes \frac{5}{12})} = \frac{\frac{21}{12}}{\frac{16}{36}} = \frac{63}{16}$.

यदि $\cos (\alpha + \beta) = \frac{3}{5}$,$\sin (\alpha - \beta) = \frac{5}{13}$ और $0 < \alpha, \beta < \frac{\pi}{4}$ है,तो $\tan (2\alpha)$ का मान ज्ञात कीजिए।

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