Bài tập 18 trang 29 SGK Toán 11 NC

Bài tập 18 trang 29 SGK Toán 11 NC

a)

\(\begin{array}{l}
\tan 3x = \tan \frac{{3\pi }}{5} \Leftrightarrow 3x = \frac{{3\pi }}{5} + k\pi \\
 \Leftrightarrow x = \frac{\pi }{5} + k\frac{\pi }{3}
\end{array}\)

b) \(\tan \left( {x - {{15}^0}} \right) = 5 \Leftrightarrow x = \alpha  + {15^0} + k{180^0}\)

trong đó \(\tan \alpha  = 5\)

c)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\tan \left( {2x - 1} \right) = \sqrt 3 \\
 \Leftrightarrow \tan \left( {2x - 1} \right) = \tan \frac{\pi }{3}
\end{array}\\
\begin{array}{l}
 \Leftrightarrow 2x - 1 = \frac{\pi }{3} + k\pi \\
 \Leftrightarrow x = \frac{\pi }{6} + \frac{1}{2} + k\frac{\pi }{2}\left( {k \in Z} \right)
\end{array}
\end{array}\)

d)

\(\begin{array}{l}
\cot 2x = \cot \left( { - \frac{1}{3}} \right) \Leftrightarrow 2x =  - \frac{1}{3} + k\pi \\
 \Leftrightarrow x =  - \frac{1}{6} + k\frac{\pi }{2}
\end{array}\)

e)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\cot \left( {\frac{x}{4} + {{20}^0}} \right) =  - \sqrt 3 \\
 \Leftrightarrow \cot \left( {\frac{x}{4} + {{20}^0}} \right) = \cot \left( { - {{30}^0}} \right)
\end{array}\\
\begin{array}{l}
 \Leftrightarrow \frac{x}{4} + {20^0} =  - {30^0} + k{180^0}\\
 \Leftrightarrow x =  - {200^0} + k{720^0}
\end{array}
\end{array}\)

f)

\(\begin{array}{l}
\cot 3x = \tan \frac{{2\pi }}{5} \Leftrightarrow \cot 3x = \cot \left( {\frac{\pi }{2} - \frac{{2\pi }}{5}} \right)\\
 \Leftrightarrow 3x = \frac{\pi }{{10}} + k\pi  \Leftrightarrow x = \frac{\pi }{{30}} + k\frac{\pi }{3}
\end{array}\)

-- Mod Toán 11