Question

Giải các phương trình:

Answer 1

j, \(cos3x-4cos2x+3cosx-4=0\)

\(\Leftrightarrow4cos^3x-3cosx-8cos^2x+4+3cosx-4=0\)

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

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

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

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

Answer 2

k, \(cos\left(x+\dfrac{\pi}{5}\right).cos\left(x-\dfrac{\pi}{5}\right)=cos\dfrac{2\pi}{5}\)

\(\Leftrightarrow\dfrac{1}{2}cos2x+\dfrac{1}{2}cos\dfrac{2\pi}{5}=cos\dfrac{2\pi}{5}\)

\(\Leftrightarrow cos2x=cos\dfrac{2\pi}{5}\)

\(\Leftrightarrow2x=\pm\dfrac{2\pi}{5}+k2\pi\)

 

\(\Leftrightarrow x=\pm\dfrac{\pi}{5}+k2\pi\)