Question

Giúp mik giải để dò đáp án mình làm ạ Câu1 trị tuyệt đối của cos x =1/ 2

Answer 1

\(\left|cosx\right|=\dfrac{1}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}cosx=\dfrac{1}{2}\\cosx=-\dfrac{1}{2}\end{matrix}\right.\)

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

\(\Leftrightarrow x=\pm\dfrac{\pi}{3}+k2\pi\)

Answer 2

\(\left|cosx\right|=\dfrac{1}{2}\)

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

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

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

\(\Rightarrow2x=\pm\dfrac{2\pi}{3}+k2\pi\)

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