a: sin 5x=sin(-2x)
=>\(\left[{}\begin{matrix}5x=-2x+k2\Omega\\5x=\Omega+2x+k2\Omega\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}7x=k2\Omega\\3x=\Omega+k2\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=\dfrac{k2\Omega}{7}\\x=\dfrac{\Omega}{3}+\dfrac{k2\Omega}{3}\end{matrix}\right.\)
b: \(cos4x=-\dfrac{\sqrt{3}}{2}\)
=>\(\left[{}\begin{matrix}4x=\dfrac{5}{6}\Omega+k2\Omega\\4x=-\dfrac{5}{6}\Omega+k2\Omega\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{24}\Omega+\dfrac{k\Omega}{2}\\x=-\dfrac{5}{24}\Omega+\dfrac{k\Omega}{2}\end{matrix}\right.\)
c: \(sin3x=cos\left(3x+40^0\right)\)
=>\(sin3x=sin\left(90^0-3x-40^0\right)=sin\left(50^0-3x\right)\)
=>\(\left[{}\begin{matrix}3x=50^0-3x+k\cdot360^0\\3x=180^0-50^0+3x+k\cdot360^0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}6x=50^0+k\cdot360^0\\0x=130^0+k\cdot360^0\left(loại\right)\end{matrix}\right.\)
=>\(x=\dfrac{25^0}{3}+k\cdot60^0\)
d: \(\left(x-30^0\right)\cdot sin2x=0\)
=>\(\left[{}\begin{matrix}x-30^0=0\\sin2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=30^0\\2x=k\cdot360^0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=30^0\\x=k\cdot180^0\end{matrix}\right.\)
e: \(sin2x=2\cdot sinx\)
=>\(2\cdot sinx\cdot cosx-2\cdot sinx=0\)
=>sinx(cosx-1)=0
=>\(\left[{}\begin{matrix}sinx=0\\cosx=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=k\Omega\\x=k2\Omega\end{matrix}\right.\Leftrightarrow x=k\Omega\)
f: \(sin2x=3\cdot cosx\)
=>\(2\cdot sinx\cdot cosx-3\cdot cosx=0\)
=>cosx(2sinx-3)=0
=>\(\left[{}\begin{matrix}cosx=0\\sinx=\dfrac{3}{2}\left(loại\right)\end{matrix}\right.\Leftrightarrow cosx=0\Leftrightarrow x=\dfrac{\Omega}{2}+k\Omega\)
g: sin x-cosx=1
=>\(\sqrt{2}\cdot sin\left(x-\dfrac{\Omega}{4}\right)=1\)
=>\(sin\left(x-\dfrac{\Omega}{4}\right)=\dfrac{1}{\sqrt{2}}\)
=>\(\left[{}\begin{matrix}x-\dfrac{\Omega}{4}=\dfrac{\Omega}{4}+k2\Omega\\x-\dfrac{\Omega}{4}=\Omega-\dfrac{\Omega}{4}+k2\Omega=\dfrac{3}{4}\Omega+k2\Omega\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\Omega}{2}+k2\Omega\\x=\Omega+k2\Omega\end{matrix}\right.\)
