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

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Solution

The correct option is A 3
$2 s i n^{2} x + \frac{2 s i n x c o s x}{2} = n s i n 2 x - 2 c o s 2 x = 2 n - 2 - \sqrt{5} \leq 2 n - 2 \leq \sqrt{5} \Rightarrow 1 - \frac{\sqrt{5}}{2} \leq n \leq 1 + \frac{\sqrt{5}}{2} ∴ (A)$

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