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Solve the equation 4cos^(2)theta+sqrt(3)...

Solve the equation `4cos^(2)theta+sqrt(3)=2(sqrt(3)+1)costheta`.

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`4cos^(2)theta+sqrt(3)=2(sqrt(3)+1)costheta`
`rArr 4cos^(2)theta+sqrt(3)=2sqrt(3)costheta+2costheta`
`rArr 4cos^(2)theta-2costheta-2sqrt(3)costheta-2sqrt(3)costheta+sqrt(3)=0`
`rArr 2costheta(2costheta-1)-sqrt(3)(2costheta-1)=0`
`rArr (2costheta-1)(2costheta-sqrt(3))=0`
Now `2costheta-1=0`
`rArr costheta=1/2=cospi/3`
`rArr theta=2npi+-pi/3`. Ans.
and `2costheta-sqrt(3)=0`
`rArr costheta=sqrt(3)/2=cospi/6`
`rArr theta=2npi+-pi/6`.
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