Bài tập 27 trang 41 SGK Toán 11 NC

Bài tập 27 trang 41 SGK Toán 11 NC

a)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
2\cos x - \sqrt 3  = 0 \Leftrightarrow \cos x = \frac{{\sqrt 3 }}{2}\\
 \Leftrightarrow \cos x = \cos \frac{\pi }{6}
\end{array}\\
{ \Leftrightarrow x =  \pm \frac{\pi }{6} + k2\pi ,k \in Z}
\end{array}\)

b)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\sqrt 3 \tan 3x - 3 = 0 \Leftrightarrow \tan 3x = \sqrt 3 \\
 \Leftrightarrow \tan 3x = \tan \frac{\pi }{3} \Leftrightarrow 3x = \frac{\pi }{3} + k\pi 
\end{array}\\
{ \Leftrightarrow x = \frac{\pi }{9} + k\frac{\pi }{3},k \in Z}
\end{array}\)

c)

\(\begin{array}{l}
\left( {\sin x + 1} \right)\left( {2\cos 2x - \sqrt 2 } \right) = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
\sin x + 1 = 0\\
2\cos 2x - \sqrt 2  = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\sin x =  - 1\\
\cos 2x = \frac{{\sqrt 2 }}{2}
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x =  - \frac{\pi }{2} + k2\pi \\
2x =  \pm \frac{\pi }{4} + k2\pi 
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x =  - \frac{\pi }{2} + k2\pi \\
x =  \pm \frac{\pi }{8} + k\pi 
\end{array} \right.
\end{array}\)

-- Mod Toán 11