If (sec alpha + tan alpha )(sec beta + tan be | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given: $(\sec \alpha + 	an \alpha )(\sec \beta + 	an \beta )(\sec \gamma + 	an \gamma ) = 	an \alpha 	an \beta 	an \gamma$ ... $(i)$Let $x =

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Given: $(\sec \alpha + 	an \alpha )(\sec \beta + 	an \beta )(\sec \gamma + 	an \gamma ) = 	an \alpha 	an \beta 	an \gamma$ ... $(i)$Let $x = (\sec \alpha - 	an \alpha )(\sec \beta - 	an \beta )(\sec \gamma - 	an \gamma )$ ... $(ii)$Multiplying equation $(i)$ and $(ii)$,we get:$(\sec^2 \alpha - 	an^2 \alpha )(\sec^2 \beta - 	an^2 \beta )(\sec^2 \gamma - 	an^2 \gamma ) = x \cdot (	an \alpha 	an \beta 	an \gamma )$Since $\sec^2 	heta - 	an^2 	heta = 1$,the left side becomes $1 \cdot 1 \cdot 1 = 1$.So,$1 = x \cdot (	an \alpha 	an \beta 	an \gamma )$$x = \frac{1}{	an \alpha 	an \beta 	an \gamma } = \cot \alpha \cot \beta \cot \gamma $

If $(\sec \alpha + \tan \alpha )(\sec \beta + \tan \beta )(\sec \gamma + \tan \gamma ) = \tan \alpha \tan \beta \tan \gamma $,then $(\sec \alpha - \tan \alpha )(\sec \beta - \tan \beta )(\sec \gamma - \tan \gamma ) = $

Similar Questions

Evaluate: $\sin \frac{\pi}{12} \sin \frac{2 \pi}{12} \sin \frac{3 \pi}{12} \sin \frac{4 \pi}{12} \sin \frac{5 \pi}{12} \sin \frac{6 \pi}{12}$

If $\frac{\cos (A+B)}{\cos (A-B)}=\frac{\sin (C+D)}{\sin (C-D)}$,then $\tan A \tan B \tan C=$

If $\tan(\pi \sin \theta) = \cot(\pi \cos \theta)$,then $\left| \cot \left( \theta - \frac{\pi}{4} \right) \right|$ is -

If $\sum_{r=1}^{50} \tan ^{-1} \frac{1}{2 r^2}=p$,then $\tan p$ is

The sum of the solutions of the equation $\cos x \cos \left(\frac{\pi}{3}-x\right) \cos \left(\frac{\pi}{3}+x\right)=\frac{1}{4}$ in the interval $(0, 2\pi)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module