Toán Lớp 11: a) sin^2x-3sinx+2=0
b) 5cosx-2sin2x=0
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Toán Lớp 11: a) sin^2x-3sinx+2=0
b) 5cosx-2sin2x=0
Comments ( 1 )
a,\\
x = \dfrac{\pi }{2} + k2\pi \,\,\,\left( {k \in Z} \right)\\
b,\\
x = \dfrac{\pi }{2} + k\pi \,\,\,\,\left( {k \in Z} \right)
\end{array}\)
a,\\
{\sin ^2}x – 3\sin x + 2 = 0\\
\Leftrightarrow \left( {{{\sin }^2}x – \sin x} \right) + \left( { – 2\sin x + 2} \right) = 0\\
\Leftrightarrow \sin x.\left( {\sin x – 1} \right) – 2.\left( {\sin x – 1} \right) = 0\\
\Leftrightarrow \left( {\sin x – 1} \right)\left( {\sin x – 2} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin x – 1 = 0\\
\sin x – 2 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\sin x = 1\\
\sin x = 2
\end{array} \right.\\
– 1 \le \sin x \le 1 \Rightarrow \sin x = 1 \Rightarrow x = \dfrac{\pi }{2} + k2\pi \,\,\,\left( {k \in Z} \right)\\
b,\\
5\cos x – 2\sin 2x = 0\\
\Leftrightarrow 5\cos x – 2.2\sin x.\cos x = 0\\
\Leftrightarrow 5\cos x – 4\sin x.\cos x = 0\\
\Leftrightarrow \cos x.\left( {5 – 4\sin x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = 0\\
5 – 4\sin x = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\cos x = 0\\
\sin x = \dfrac{5}{4}
\end{array} \right.\\
– 1 \le \sin x \le 1 \Rightarrow \cos x = 0 \Leftrightarrow x = \dfrac{\pi }{2} + k\pi \,\,\,\,\left( {k \in Z} \right)
\end{array}\)