Question #c7fbc

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Answer 1 · 2017-03-07T15:50:28

$3sin^2theta-sinthetacostheta-4cos^2theta=0$

$=>(3sin^2theta)/cos^2theta-(sinthetacostheta)/cos^2theta-(4co s^2theta)/cos^2theta=0$

$=>3tan^2theta-tantheta-4=0$

$=>3tan^2theta-4tantheta+3tantheta-4=0$

$=>tantheta(3tantheta-4)+1(3tantheta-4)=0$

$=>(3tantheta-4)(tantheta+1)=0$

When

$3tantheta-4=0$

$=>tantheta=4/3=tan(tan^-1(4/3))$

$=>theta=npi+tan^-1(4/3)" where "n in ZZ$

When

$tantheta+1=0$

$=>tantheta=-1=tan(-pi/4)$

$=>theta=npi-pi/4" where "n in ZZ$