यदि (sec alpha + tan alpha )(sec beta + tan b | vedclass

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Question

(A) दिया है: $(\sec \alpha + 	an \alpha )(\sec \beta + 	an \beta )(\sec \gamma + 	an \gamma ) = 	an \alpha 	an \beta 	an \gamma$ ... $(i)$माना $

Vedclass · Accepted Answer

$\cot \alpha \cot \beta \cot \gamma $

Vedclass · Answer

(A) दिया है: $(\sec \alpha + 	an \alpha )(\sec \beta + 	an \beta )(\sec \gamma + 	an \gamma ) = 	an \alpha 	an \beta 	an \gamma$ ... $(i)$माना $x = (\sec \alpha - 	an \alpha )(\sec \beta - 	an \beta )(\sec \gamma - 	an \gamma )$ ... $(ii)$समीकरण $(i)$ और $(ii)$ का गुणा करने पर:$(\sec^2 \alpha - 	an^2 \alpha )(\sec^2 \beta - 	an^2 \beta )(\sec^2 \gamma - 	an^2 \gamma ) = x \cdot (	an \alpha 	an \beta 	an \gamma )$चूंकि $\sec^2 	heta - 	an^2 	heta = 1$,बायां पक्ष $1 \cdot 1 \cdot 1 = 1$ हो जाता है।अतः,$1 = x \cdot (	an \alpha 	an \beta 	an \gamma )$$x = \frac{1}{	an \alpha 	an \beta 	an \gamma } = \cot \alpha \cot \beta \cot \gamma $

यदि $(\sec \alpha + \tan \alpha )(\sec \beta + \tan \beta )(\sec \gamma + \tan \gamma ) = \tan \alpha \tan \beta \tan \gamma $ है,तो $(\sec \alpha - \tan \alpha )(\sec \beta - \tan \beta )(\sec \gamma - \tan \gamma ) = $

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