Question

Giải các phương trình sau: 

\(a,cos2x+4cosx+1=0\)

\(b,cos^22x=\dfrac{1}{4}\)

Answer 1

a, \(cos2x+4cosx+1=0\)

\(\Leftrightarrow2cos^2x+4cosx=0\)

\(\Leftrightarrow2cosx\left(cosx+2\right)=0\)

\(\Leftrightarrow cosx=0\)

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

Answer 2

b, \(cos^22x=\dfrac{1}{4}\)

\(\Leftrightarrow4cos^22x-1=0\)

\(\Leftrightarrow\left(2cosx-1\right)\left(2cosx+1\right)=0\)

\(\Leftrightarrow cosx=\pm\dfrac{1}{2}\)

\(\Leftrightarrow x=\pm\dfrac{\pi}{3}+k\pi\)