Toán Lớp 11: sinx/2+cosx/2-sinx-1=0. mọi người giúp mik vs mik cần gấp lắm
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Toán Lớp 11: sinx/2+cosx/2-sinx-1=0. mọi người giúp mik vs mik cần gấp lắm
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$x = \pi + k4\pi $
\left( {\sin \frac{x}{2} + \cos \frac{x}{2}} \right).\left( { – \sin \frac{x}{2} – \cos \frac{x}{2} + 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin \frac{x}{2} = – \cos \frac{x}{2}\\
\sin \frac{x}{2} + \cos \frac{x}{2} = 1
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\tan \frac{x}{2} = – 1\\
\sqrt 2 .\sin \left( {\frac{x}{2} + \frac{\pi }{4}} \right) = 1
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = – \frac{\pi }{2} + k2\pi \\
\sin \left( {\frac{x}{2} + \frac{\pi }{4}} \right) = \frac{1}{{\sqrt 2 }}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = – \frac{\pi }{2} + k2\pi \\
\left[ \begin{array}{l}
x = k4\pi \\
x = \pi + k4\pi
\end{array} \right.
\end{array} \right.
\end{array}\]