Solve : `3-2 cos theta -4 sin theta - cos 2theta+sin 2theta=0`.

Answer

`theta=(4n+1)(pi)/(2)` or `theta=2n pi`

Explanation

`3-2 cos theta-4 sin theta -cos 2theta + sin 2theta =0`
`rArr 3-2 cos theta -4 sin theta -1+2 sin^(2)theta + 2 sin theta cos theta = 0`
`rArr 2+2 sin^(2) theta -4 sin thetas +2 cos theta (sin theta - 1) = 0`
`rArr 2(sin^(2) theta-2sin thetas +1)+2 cos theta(sin theta -1) = 0`
`rArr 2(sin theta -1)^(2)+2 cos theta (sin theta -1)=0`
`rArr (sin theta -1) (sin theta -1+cos theta) = 0`
`rArr sin theta = 1` or `sin theta + cos theta =1`
`rArr theta =(4n+1)(pi)/(2)` or `theta = 2n pi, n in Z`