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

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Question

दिया है : $(\sec \alpha  + 	an \alpha )(\sec \beta  + 	an \beta )(\sec \gamma  + 	an \gamma )$

$ = 	an \alpha 	an \beta 	an \g

Vedclass · Accepted Answer

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

Vedclass · Answer

दिया है : $(\sec \alpha  + 	an \alpha )(\sec \beta  + 	an \beta )(\sec \gamma  + 	an \gamma )$

$ = 	an \alpha 	an \beta 	an \gamma $          ...$(i)$

माना $x = (\sec \alpha  - 	an \alpha )(\sec \beta  - 	an \beta )(\sec \gamma  - 	an \gamma )$ ...$(ii)$

समी. $(i)$ व $(ii)$ को गुणा करने पर,

$({\sec ^2}\alpha  - {	an ^2}\alpha )({\sec ^2}\beta  - {	an ^2}\beta )({\sec ^2}\gamma  - {	an ^2}\gamma )$

$ = x.(	an \alpha 	an \beta 	an \gamma )$

$ \Rightarrow x = \frac{1}{{	an \alpha 	an \beta 	an \gamma }}$,

$	herefore x = \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 $, तब $(\sec \alpha - \tan \alpha )(\sec \beta - \tan \beta )$$(\sec \gamma - \tan \gamma ) = $

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