If {tan ^2}alpha {tan ^2}beta + {tan ^2}beta | vedclass

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

Question

(c) ${\sin ^2}\alpha + {\sin ^2}\beta + {\sin ^2}\gamma $

$ = \frac{{{{	an }^2}\alpha }}{{1 + {{	an }^2}\alpha }} + \frac{{{{	an }^2}\beta }}{{1

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(c) ${\sin ^2}\alpha + {\sin ^2}\beta + {\sin ^2}\gamma $

$ = \frac{{{{	an }^2}\alpha }}{{1 + {{	an }^2}\alpha }} + \frac{{{{	an }^2}\beta }}{{1 + {{	an }^2}\beta }} + \frac{{{{	an }^2}\gamma }}{{1 + {{	an }^2}\gamma }}$

$ = \frac{x}{{1 + x}} + \frac{y}{{1 + y}} + \frac{z}{{1 + z}}$ $(x = {	an ^2}\alpha ,\,y = {	an ^2}\beta ,\,z = {	an ^2}\gamma )$

$ = \frac{{(x + y + z) + (xy + yz + zx + 2xyz) + xy + yz + zx + xyz}}{{(1 + x)(1 + y)(1 + z)}}$ 

$ = \frac{{1 + x + y + z + xy + yz + zx + xyz}}{{(1 + x)(1 + y)(1 + z)}} = 1$       $( \because xy + yz + zx + 2xyz = 1)$

If ${\tan ^2}\alpha {\tan ^2}\beta + {\tan ^2}\beta {\tan ^2}\gamma + {\tan ^2}\gamma {\tan ^2}\alpha $$ + 2{\tan ^2}\alpha {\tan ^2}\beta {\tan ^2}\gamma = 1,$ then the value of ${\sin ^2}\alpha + {\sin ^2}\beta + {\sin ^2}\gamma $ is

Similar Questions

Which of the following relations is correct

If $\tan \theta = - \frac{1}{{\sqrt {10} }}$ and $\theta $ lies in the fourth quadrant, then $\cos \theta = $

If $\sin \theta + \cos \theta = m$ and $\sec \theta + {\rm{cosec}}\theta = n$, then $n(m + 1)(m - 1) = $

$\tan 1^\circ \tan 2^\circ \tan 3^\circ \tan 4^\circ ........\tan 89^\circ = $

Find the values of other five trigonometric functions if $\tan x=-\frac{5}{12}, x$ lies in second quadrant.