Question

Giải phương trình sau: cos²x = \(\dfrac{1}{4}\)

Answer 1

\(cos^2x=\dfrac{1}{4}\)

\(\Leftrightarrow\dfrac{1}{2}cos2x+\dfrac{1}{2}=\dfrac{1}{4}\)

\(\Leftrightarrow cos2x=-\dfrac{1}{2}\)

\(\Rightarrow\left[{}\begin{matrix}2x=\dfrac{2\pi}{3}+k2\pi\\2x=-\dfrac{2\pi}{3}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{3}+k\pi\\x=-\dfrac{\pi}{3}+k\pi\end{matrix}\right.\)

Answer 2

\(\cos^2x=\dfrac{1}{4}\Leftrightarrow\sqrt{\cos^2x}=\sqrt{\dfrac{1}{4}}\)

\(\Leftrightarrow\cos x=\dfrac{1}{2}\Leftrightarrow\cos x=\cos\dfrac{\pi}{3}\)

\(\Leftrightarrow x=\pm\dfrac{\pi}{3}+k2\pi\) \((k\in \mathbb Z)\)