giải phương trình sin3x + cos3x = căn 2 giải phương trình 2sin hình x + căn 3 sin2x =3 giải phương trình căn 3 cos ( x + pi/2 ) + sin ( x – pi2 ) = 2s

Đáp án:

$\begin{array}{l}
a)\sin 3x + \cos 3x = \sqrt 2 \\
 \Rightarrow \sqrt 2 .\sin \left( {3x + \dfrac{\pi }{4}} \right) = \sqrt 2 \\
 \Rightarrow \sin \left( {3x + \dfrac{\pi }{4}} \right) = 1\\
 \Rightarrow 3x + \dfrac{\pi }{4} = \dfrac{\pi }{2} + k2\pi \\
 \Rightarrow 3x = \dfrac{\pi }{4} + k2\pi \\
 \Rightarrow x = \dfrac{\pi }{{12}} + \dfrac{{k2\pi }}{3}\\
Vay\,x = \dfrac{\pi }{{12}} + \dfrac{{k2\pi }}{3}\\
b)2{\sin ^2}x + \sqrt 3 \sin 2x = 3\\
 \Rightarrow 2{\sin ^2}x – 1 + \sqrt 3 \sin 2x = 2\\
 \Rightarrow  – \cos 2x + \sqrt 3 \sin 2x = 2\\
 \Rightarrow \dfrac{{\sqrt 3 }}{2}\sin 2x – \dfrac{1}{2}\cos 2x = 1\\
 \Rightarrow \sin \left( {2x – \dfrac{\pi }{3}} \right) = 1\\
 \Rightarrow 2x – \dfrac{\pi }{3} = \dfrac{\pi }{2} + k2\pi \\
 \Rightarrow x = \dfrac{{5\pi }}{{12}} + k\pi \\
Vay\,x = \dfrac{{5\pi }}{{12}} + k\pi \\
c)\\
\sqrt 3 \cos \left( {x + \dfrac{\pi }{2}} \right) + \sin \left( {x – \dfrac{\pi }{2}} \right) = 2\sin 2x\\
 \Rightarrow \sqrt 3 \sin x + \cos x = 2\sin 2x\\
 \Rightarrow \dfrac{{\sqrt 3 }}{2}\sin x + \dfrac{1}{2}\cos x = \sin 2x\\
 \Rightarrow \sin \left( {x + \dfrac{\pi }{3}} \right) = \sin 2x\\
 \Rightarrow \left[ \begin{array}{l}
x + \dfrac{\pi }{3} = 2x + k2\pi \\
x + \dfrac{\pi }{3} = \pi  – 2x + k2\pi 
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{3} – k2\pi \\
x = \dfrac{{2\pi }}{9} + \dfrac{{k2\pi }}{3}
\end{array} \right.
\end{array}$