Question #6dd1a

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Answer 1 · 2017-03-03T13:27:16

#sin2x=4cos^2x-6sin^2x#

#=>6sin^2x+2sinxcosx-4cos^2x=0#

#=>3sin^2x+sinxcosx-2cos^2x=0#

#=>(3sin^2x)/cos^2x+(sinxcosx)/cos^2x-(2cos^2x)/cos^2x=0#

#=>3tan^2x+tanx-2=0#

#=>3tan^2x+3tanx-2tanx-2=0#

#=>3tanx(tanx+1)-2(tanx+1)=0#

#=>(tanx+1)(3tanx-2)=0#

When #tanx+1=0#

#=>tanx=-1=tan(pi-pi/4)=tan(2pi-pi/4)#

So

#x=(3pi)/4 and (7pi)/4#

#=>x=135^@ and 315^@#

Again

#3tanx -2 = 0#

#=>tanx=2/3=tan(tan^-1(2/3))=tan33.7^@#

So

#x= 33.7^@ and (180+33.7)=213.7^@#