જો {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$       $( \because xy + yz + zx + 2xyz = 1)$

જો ${\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,$ તો ${\sin ^2}\alpha + {\sin ^2}\beta + {\sin ^2}\gamma =.........$

Similar Questions

${\sin ^6}\theta + {\cos ^6}\theta + 3{\sin ^2}\theta {\cos ^2}\theta = $

ત્રિકોણમિતિય વિધેયોનાં મૂલ્યો શોધો. $\sin \left(-\frac{11 \pi}{3}\right)$

જો $\tan \theta = - \frac{1}{{\sqrt {10} }}$ અને $\theta $ એ ચોથા ચરણમાં હોય તો $\cos \theta = $

અંશ માપ શોધો. ( $\pi=\frac{22}{7}$ લો. ) $\frac{11}{16}$

જો $0 < x < \pi $ અને $\cos x + \sin x = \frac{1}{2}$ તો $\tan x$ મેળાવે. . .