Toán Lớp 11: $2(cos4x – sin4x) + \sqrt{3} = 0$
Giair pt
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Toán Lớp 11: $2(cos4x – sin4x) + \sqrt{3} = 0$
Giair pt
Comments ( 2 )
2\left( {\cos 4x – \sin 4x} \right) + \sqrt 3 = 0\\
\Leftrightarrow \cos 4x – \sin 4x = – \dfrac{{\sqrt 3 }}{2}\\
\Rightarrow \sin 4x – \cos 4x = \dfrac{{\sqrt 3 }}{2}\\
\Leftrightarrow \sqrt 2 \sin \left( {4x – \dfrac{\pi }{4}} \right) = \dfrac{{\sqrt 3 }}{2}\\
\Leftrightarrow \sin \left( {4x – \dfrac{\pi }{4}} \right) = \dfrac{{\sqrt 6 }}{4}\\
\Leftrightarrow \left[ \begin{array}{l}
4x – \dfrac{\pi }{4} = \arcsin \dfrac{{\sqrt 6 }}{4} + k2\pi \\
4x – \dfrac{\pi }{4} = \pi – \arcsin \dfrac{{\sqrt 6 }}{4} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{{16}} + \dfrac{{\arcsin \dfrac{{\sqrt 6 }}{4}}}{4} + \dfrac{{k\pi }}{2}\\
x = \dfrac{{5\pi }}{{16}} – \dfrac{{\arcsin \dfrac{{\sqrt 6 }}{4}}}{4} + \dfrac{{k\pi }}{2}
\end{array} \right.\left( {k \in \mathbb Z} \right)
\end{array}$