Question

cos3x-cos3x-2sin2x=0​

Answer 1

$(Cosx-Cos3x)-2Sin2x=0\\\\-2Sin\frac{x+3x}{2}Sin\frac{x-3x}{2}-2Sin2x=0\\\\2Sin2xSinx-2Sin2x=0\\\\Sin2xSinx-Sin2x=0\\\\Sin2x(Sinx-1)=0\\\\\left[\begin{array}{ccc}Sin2x=0\\Sinx-1=0\end{array}\right\\\\\\\left[\begin{array}{ccc}2x=\pi n,n\in Z \\Sinx=1\end{array}\right\\\\\\\left[\begin{array}{ccc}x=\frac{\pi n }{2},n\in Z  \\x=\frac{\pi }{2}+2\pi n,n\in Z  \end{array}\right\\\\Otvet:\boxed{\frac{\pi n}{2},n\in Z}$