Question

Answer 1

1.

\(cos3x-4cos2x+3cosx-4=0\)

\(\Leftrightarrow4cos^3x-4cos2x-4=0\)

\(\Leftrightarrow4cos^3x-8cos^2x=0\)

\(\Leftrightarrow4cos^2x\left(cosx-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\cosx=2\left(l\right)\end{matrix}\right.\)

\(\Leftrightarrow x=\dfrac{\pi}{2}+k\pi\)

Answer 2

2.

\(sin3x+cos2x=1+2sinx.cos2x\)

\(\Leftrightarrow sin3x-sin^2x=sin3x-sinx\)

\(\Leftrightarrow sin^2x-sinx=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sinx=0\\sinx=1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)