The equation $4 {sin}^{2} x + 4 sin x + a^{2} - 3 = 0$ has a solution if

- 2 \leq a \leq 2

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- 1 \leq a \leq 1

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- 3 \leq a \leq 3

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- 4 \leq a \leq 4

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Solution

The correct option is B $- 2 \leq a \leq 2$
we get
$(2 sin x + 1)^{2} = 4 - a^{2}$
so $0 ⩽ 4 - a^{2} ⩽ 9$

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