Toán Lớp 11: Giải phương trình
sin2x – cos2x = -1
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Toán Lớp 11: Giải phương trình
sin2x – cos2x = -1
Comments ( 2 )
\sin 2x – \cos 2x = 1\\
\Leftrightarrow \frac{1}{{\sqrt 2 }}\cos 2x – \frac{1}{{\sqrt 2 }}\sin 2x = \frac{1}{{\sqrt {2x} }}\\
\Leftrightarrow \cos \left( {2x + \frac{\pi }{4}} \right) = \frac{1}{{\sqrt 2 }}\\
\Leftrightarrow \left[ \begin{array}{l}
2x + \frac{\pi }{4} = \frac{\pi }{2} + k2\pi \\
2x + \frac{\pi }{4} = – \frac{\pi }{2} + k2\pi
\end{array} \right.\,\, \Leftrightarrow \left[ \begin{array}{l}
x = k\pi \\
x = – \frac{\pi }{4} + k\pi
\end{array} \right.
\end{array}\]