Ngân hàng bài tập
B
Phương trình \(\sin x\cdot\cos\dfrac{\pi}{5}+\cos x\cdot\sin\dfrac{\pi}{5}=\dfrac{1}{2}\) có nghiệm là
 | \(\left[\begin{array}{l}x=-\dfrac{\pi}{30}+k2\pi\\ x=\dfrac{19\pi}{30}+k2\pi\end{array}\right.\,(k\in\mathbb{Z})\) |
 | \(\left[\begin{array}{l}x=\dfrac{\pi}{30}+k2\pi\\ x=-\dfrac{19\pi}{30}+k2\pi\end{array}\right.\,(k\in\mathbb{Z})\) |
 | \(\left[\begin{array}{l}x=\dfrac{\pi}{6}+k2\pi\\ x=\dfrac{5\pi}{6}+k2\pi\end{array}\right.\,(k\in\mathbb{Z})\) |
 | \(\left[\begin{array}{l}x=-\dfrac{\pi}{30}+k2\pi\\ x=-\dfrac{19\pi}{30}+k2\pi\end{array}\right.\,(k\in\mathbb{Z})\) |
1 lời giải
Chọn phương án A.
\(\begin{eqnarray*}
&\sin x\cdot\cos\dfrac{\pi}{5}+\cos x\cdot\sin\dfrac{\pi}{5}&=\dfrac{1}{2}\\
\Leftrightarrow&\sin\left(x+\dfrac{\pi}{5}\right)&=\dfrac{1}{2}\\
\Leftrightarrow&\left[\begin{array}{l}x+\dfrac{\pi}{5}=\dfrac{\pi}{6}+k2\pi\\ x+\dfrac{\pi}{5}=\dfrac{5\pi}{6}+k2\pi\end{array}\right.\\
\Leftrightarrow&\left[\begin{array}{l}x=-\dfrac{\pi}{30}+k2\pi\\ x=\dfrac{19\pi}{30}+k2\pi\end{array}\right.\,(k\in\mathbb{Z})
\end{eqnarray*}\)