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 equations $(i)$ 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 $\sec^2 	heta - 	an^2 	heta = 1$ for any angle $	heta$,the left side becomes $(1)(1)(1) = 1$.Therefore,$1 = x \cdot (	an \alpha 	an \beta 	an \gamma )$.$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

The angle of elevation of the top of an unfinished tower at a point $120\, m$ from its base is $45^{\circ}$. How much higher must the tower be raised so that its angle of elevation at the same point be $60^{\circ}$? (in $m$)

If $A + B + C = \frac{3\pi}{2},$ then $\cos 2A + \cos 2B + \cos 2C = $

$\Delta XYZ$ is right-angled at $Y$. If $\cos X = \frac{3}{5}$,then what is the value of $\operatorname{cosec} Z$?

The equation $\sec^2 \theta = \frac{4xy}{(x + y)^2}$ is only possible when

$2\cos^2 \theta - 2\sin^2 \theta = 1$,then $\theta = \dots \dots ^\circ$

Vedclass Test Series

Exam Paper Generator

Online Exam Module