The number of solutions of the pair of equations `2sin^2 theta - cos(2 theta)=0,2cos^2 theta-3sin theta=0` in the interval `[0,2pi]` is

Explanation

`2sinn^2theta-cos2theta=0`

`2sin^2theta-(1-2sin^2theta)=0`

`2sin^2theta-1+2sin^2theta=0`

`4sin^2theta=1/e`

`sin^2theta=1/4`

`sintheta=1/2,-1/2`

`2cos^2theta-3sintheta=0`

`2(1-sin^2theta)-3sintheta=0`

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