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Sum of integral values of n such that $\sin x (2 \sin x + \cos x) = n$ has at least one real solution is

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Correct option is C

2sin2⁡x+2sin⁡xcos⁡x2=n⇒sin⁡2x+2(1−cos⁡2x)=2n⇒sin⁡2x−2cos⁡2x=2(n−1)⇒ −5≤2n−2≤5⇒ 1−52≤n≤1+52Integral values of n are 0, 1, 2.

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Sum of integral values of n such that sinx (2 sin x + cos x) = n has at least one real solution is

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Sum of integral values of n such that $\sin x (2 \sin x + \cos x) = n$ has at least one real solution is