Toán Lớp 11: 2sinxsin3x+cos2x=-3
giải pt lượng giác chi tiết
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: 2sinxsin3x+cos2x=-3
giải pt lượng giác chi tiết
Comments ( 1 )
2\sin x.\sin y = – \left[ {\cos \left( {x + y} \right) – \cos \left( {x – y} \right)} \right]\\
\cos 2x = 2{\cos ^2}x – 1\\
2\sin x.\sin 3x + \cos 2x = – 3\\
\Leftrightarrow – \left[ {\cos \left( {x + 3x} \right) – \cos \left( {x – 3x} \right)} \right] + \cos 2x = – 3\\
\Leftrightarrow – \left( {\cos 4x – \cos \left( { – 2x} \right)} \right) + \cos 2x = – 3\\
\Leftrightarrow – \left( {\cos 4x – \cos 2x} \right) + \cos 2x = – 3\\
\Leftrightarrow – \cos 4x + \cos 2x + \cos 2x = – 3\\
\Leftrightarrow – \left( {2{{\cos }^2}2x – 1} \right) + 2\cos 2x + 3 = 0\\
\Leftrightarrow – 2{\cos ^2}2x + 1 + 2\cos 2x + 3 = 0\\
\Leftrightarrow – 2{\cos ^2}2x + 2\cos 2x + 4 = 0\\
\Leftrightarrow {\cos ^2}2x – \cos 2x – 2 = 0\\
\Leftrightarrow \left( {\cos 2x – 2} \right)\left( {\cos 2x + 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cos 2x – 2 = 0\\
\cos 2x + 1 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\cos 2x = 2\\
\cos 2x = – 1
\end{array} \right.\\
– 1 \le \cos 2x \le 1 \Rightarrow \cos 2x = – 1\\
\cos 2x = – 1\\
\Leftrightarrow 2x = \pi + k2\pi \\
\Leftrightarrow x = \dfrac{\pi }{2} + k\pi \,\,\,\left( {k \in Z} \right)
\end{array}\)