Toán Lớp 11: Giải giúp em bài này ạ
(2sinx -cosx).(1+ cosx) = sin^2(x)
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 11: Giải giúp em bài này ạ
(2sinx -cosx).(1+ cosx) = sin^2(x)
Comments ( 2 )
\left( {2\sin x – \cos x} \right)\left( {1 + \cos x} \right) = {\sin ^2}x\\
\Leftrightarrow 2\sin x + 2\sin x\cos x – \cos x – {\cos ^2}x = {\sin ^2}x\\
\Leftrightarrow 2\sin x + 2\sin x\cos x – \cos x – \left( {{{\sin }^2}x + {{\cos }^2}x} \right) = 0\\
\Leftrightarrow 2\sin x + 2\sin x\cos x – \cos x – 1 = 0\\
\Leftrightarrow 2\sin x\left( {1 + \cos x} \right) – \left( {1 + \cos x} \right) = 0\\
\Leftrightarrow \left( {1 + \cos x} \right)\left( {2\sin x – 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = – 1\\
\sin x = \dfrac{1}{2}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \pi + k2\pi \\
x = \dfrac{\pi }{6} + k2\pi \\
x = \dfrac{{5\pi }}{6} + k2\pi
\end{array} \right.\left( {k \in \mathbb{Z}} \right)
\end{array}$