If `A=2sin^2theta-cos2theta` ,the `A` lies in the interval
(a) `[-1,3]`
(b) `[1,2]`
(c) `[-2,4]`
(d) none of these

Explanation

`A=2sin^2 theta-cos 2theta`

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

`=4sin^2theta-1`

We know that `0<=sin^2 theta<=1`

`=>4 xx 0<=4xx sin^2 theta<=4 xx 1`

`=>0<=4sin^2theta<=4`

`=>0-1<=4sin^2theta-1<=4-1`

`=>-1<=4sin^2theta-1<=3`
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