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

Explanation

Given,

`A=2 sin^2theta−cos ^2theta`

`=2 sin^2theta−(1−2 sin^2theta)`

`=4 sin^2theta−1`

We know range of `sinx` is
` 0≤ sin^2theta≤1`

`⇒ 4×0le4×sin^2thetale4×1`

`=> 0le4 sin^2theta le4`

`=> 0−1le4 sin^2thetale4`

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