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If $y = 2 \sin^{2} α - \cos 2 α$ then $y$ lies in the interval

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$- 1 \leq y \leq 3$

$- 1 \leq y \leq 1$

$0 \leq y \leq 2$

$1 \leq y \leq 2$

answer is A.

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Detailed Solution

$y = 2 \sin^{2} α - \cos 2 α = 1 - \cos 2 α - \cos 2 α = 1 - 2 \cos 2 α \cos 2 α \in [- 1, 1] - 2 \cos 2 α \in [- 2, 2] 1 - 2 \cos 2 α \in [- 1, 3] y \in [- 1, 3]$

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