-cosx + căn 3 /3 sinx -1 =0 có tất cả các nghiệm là : giúp mk vs 13/08/2021 Bởi Rylee -cosx + căn 3 /3 sinx -1 =0 có tất cả các nghiệm là : giúp mk vs
Đáp án: $\begin{array}{l} – \cos x + \frac{{\sqrt 3 }}{3}.\sin x – 1 = 0\\ \Rightarrow – \cos x + \frac{{\sqrt 3 }}{3}\sin x = 1\\ \Rightarrow – \frac{{\sqrt 3 }}{2}\cos x + \frac{1}{2}\sin x = \frac{{\sqrt 3 }}{2}\\ \Rightarrow \cos \frac{{5\pi }}{6}.\cos x + \sin \frac{{5\pi }}{6}.\sin x = \frac{{\sqrt 3 }}{2}\\ \Rightarrow \cos \left( {x – \frac{{5\pi }}{6}} \right) = \cos \frac{\pi }{6}\\ \Rightarrow \left[ \begin{array}{l}x – \frac{{5\pi }}{6} = \frac{\pi }{6} + k2\pi \\x – \frac{{5\pi }}{6} = – \frac{\pi }{6} + k2\pi \end{array} \right.\left( {k \in Z} \right)\\ \Rightarrow \left[ \begin{array}{l}x = \pi + k2\pi \\x = \frac{{2\pi }}{3} + k2\pi \end{array} \right.\left( {k \in Z} \right)\end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
– \cos x + \frac{{\sqrt 3 }}{3}.\sin x – 1 = 0\\
\Rightarrow – \cos x + \frac{{\sqrt 3 }}{3}\sin x = 1\\
\Rightarrow – \frac{{\sqrt 3 }}{2}\cos x + \frac{1}{2}\sin x = \frac{{\sqrt 3 }}{2}\\
\Rightarrow \cos \frac{{5\pi }}{6}.\cos x + \sin \frac{{5\pi }}{6}.\sin x = \frac{{\sqrt 3 }}{2}\\
\Rightarrow \cos \left( {x – \frac{{5\pi }}{6}} \right) = \cos \frac{\pi }{6}\\
\Rightarrow \left[ \begin{array}{l}
x – \frac{{5\pi }}{6} = \frac{\pi }{6} + k2\pi \\
x – \frac{{5\pi }}{6} = – \frac{\pi }{6} + k2\pi
\end{array} \right.\left( {k \in Z} \right)\\
\Rightarrow \left[ \begin{array}{l}
x = \pi + k2\pi \\
x = \frac{{2\pi }}{3} + k2\pi
\end{array} \right.\left( {k \in Z} \right)
\end{array}$