Nghiệm của phương trình \(\cos 2x + 5\sin x - 4 = 0\) là

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\[x = \frac{\pi }{2} + k\pi \].

\[x = - \frac{\pi }{2} + k\pi \].

\(x = k2\pi \).

\(x = \frac{\pi }{2} + k2\pi .\)

Giải thích

Ta có \[\cos 2x + 5\sin x - 4 = 0 \Leftrightarrow 1 - 2{\sin ^2}x + 5\sin x - 4 = 0\]

\[ \Leftrightarrow - 2{\sin ^2}x + 5\sin x - 3 = 0 \Leftrightarrow \left[ {\begin{array}{*{20}{l}}{\sin x = 1}\\{\sin {\mkern 1mu} x = \frac{3}{2}{\mkern 1mu} {\mkern 1mu} \left( {vo{\mkern 1mu} {\mkern 1mu} nghiem} \right)}\end{array}} \right. \Leftrightarrow x = \frac{\pi }{2} + k2\pi ,{\mkern 1mu} {\mkern 1mu} \,k \in \mathbb{Z}.\]Chọn D.