36.
\(sin2x-cos3x=0\)
\(\Leftrightarrow cos\left(\dfrac{\pi}{2}-2x\right)=cos3x\)
\(\Leftrightarrow\dfrac{\pi}{2}-2x=\pm3x+k2\pi\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{10}-\dfrac{k2\pi}{5}\\x=-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)
37.
\(sinx+sin3x=0\)
\(\Leftrightarrow2sin2x.cosx=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin2x=0\\cosx=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{k\pi}{2}\\x=\dfrac{\pi}{2}+k\pi\end{matrix}\right.\)
`sin2x-cos3x=0`
`<=>sin2x=cos3x `
`<=>cos(π/2-2x)=cos3x`
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{\text{π}}{2}-2x=3x+k2\text{π}\\\dfrac{\text{π}}{2}-2x=-3x+k2\text{π}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{10}+\dfrac{k2\pi}{5}\\x=-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)
`sinx+sin3x=0`
`<=>sinx=sin(-3x)`
`<=>[(x=-3x+k2π),(x=π+3x+k2π):}`
`<=>[(x=k π/2),(x=-π/2+kπ):}`
