Question

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

• A. 3
• B. 1
• C. 2
• D. 0

Answer 1

The correct option is A

3

$2si{n}^{2}x+\frac{2sinxcosx}{2}=nsin2x-2cos2x=2n-2-\sqrt{5}\le 2n-2\le \sqrt{5}\Rightarrow 1-\frac{\sqrt{5}}{2}\le n\le 1+\frac{\sqrt{5}}{2}$