General solution of \( 1+\sin (x) \sin ^{2}\left(\frac{x}{2}\right)=0 \) is-

A \( n \pi+\frac{\pi}{4} \)

B \( 2 n \pi+\frac{\pi}{4} \)

C \( 2 n \pi+\frac{\pi}{6} \)

D no solution

Solution

Correct Answer: Option D

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