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simplify 2sin^2`theta` +2sin2`theta` +cos^2`theta` =0

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dimakatso-13 | eNotes Newbie

Posted July 15, 2013 at 2:07 PM via web

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simplify

2sin^2`theta` +2sin2`theta` +cos^2`theta` =0

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aruv | High School Teacher | Valedictorian

Posted July 15, 2013 at 3:32 PM (Answer #1)

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`2sin^2(theta)+2sin(2theta)+cos^2(theta)=0`

`sin^2(theta)+4sin(theta)cos(theta)+sin^2(theta)+cos^2(theta)=0`

`sin^2(theta)+4sin(theta) cos(theta)+1=0`

`` Divide both side by `sin^2(theta)`

`1+4cot(theta)+1/(sin^2(theta))=0`

`1+4cot(theta)+cosec^2(theta)=0```

`1+4cot(theta)+1+cot^2(theta)=0`

`Let`

`cot(theta)=x`

Then

`1+4x+1+x^2=0`

`x^2+4x+2=0`

`x=(-4+-sqrt(16-8))/2`

`x=(-4+-sqrt(8))/2`

`x=(-2+-sqrt(2))`

`x=-3.414 ,-.586`

`ifcot(theta)=-3.414`

`tan(theta)=-.293`

`tan(theta)=-tan(16.326^o)`

`tan(theta)=tan(180-16.326^o)=tan(163.674^o)`

`tan(theta)=tan((91pi)/100)`

`theta=npi+(91pi)/100`     n is  an integer.

if `cot(theta)=-.586`

`tan(theta)=-1.706`

`=-tan(59.63^o)`

`=tan(180-59.63^o)=tan(120.37^o)`

`=tan((67pi)/100)`

`theta=mpi+(67pi)/100`   ,m is an integer.

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