Toán Lớp 11: Cosx-√3sinx =√2 khai triển biểu thức lượng giác
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Toán Lớp 11: Cosx-√3sinx =√2 khai triển biểu thức lượng giác
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x = – \dfrac{\pi }{{12}} + k2\pi \\
x = – \dfrac{{7\pi }}{{12}} + k2\pi
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)\]
\cos x – \sqrt 3 \sin x = \sqrt 2 \\
\Leftrightarrow \dfrac{1}{2}\cos x – \dfrac{{\sqrt 3 }}{2}\sin x = \dfrac{{\sqrt 2 }}{2}\\
\Leftrightarrow \cos x.\cos \dfrac{\pi }{3} – \sin x.\sin \dfrac{\pi }{3} = \dfrac{{\sqrt 2 }}{2}\\
\Leftrightarrow \cos \left( {x + \dfrac{\pi }{3}} \right) = \dfrac{{\sqrt 2 }}{2}\\
\Leftrightarrow \cos \left( {x + \dfrac{\pi }{3}} \right) = \cos \dfrac{\pi }{4}\\
\Leftrightarrow \left[ \begin{array}{l}
x + \dfrac{\pi }{3} = \dfrac{\pi }{4} + k2\pi \\
x + \dfrac{\pi }{3} = – \dfrac{\pi }{4} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = – \dfrac{\pi }{{12}} + k2\pi \\
x = – \dfrac{{7\pi }}{{12}} + k2\pi
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)
\end{array}\)