Phương trình

D

- Hướng dẫn giải

Đáp án D

PT 

$$\begin{gathered} \iff 1-2{\sin }^{2}x+4\sin x+5=0 \\ \iff {\sin }^{2}x-2\sin x-3=0\iff \left[\begin{array}{l}\sin x=-1\\ \sin x=3\end{array}\right. \end{gathered}$$

$\Rightarrow \sin x=-1\iff x=-\frac{\pi }{2}+k2\pi \left(k\in \mathbb{Z}\right)$

Vì

$$\begin{gathered} x\in \left(0;10\pi \right)\iff 0<-\frac{\pi }{2}+k2\pi <10\pi \\ \iff \frac{1}{4}<k<\frac{21}{4}\Rightarrow k\in \left\{1;2;3;4;5\right\} \end{gathered}$$