Question

\(\sin^22x+\cos^2x=1\)

Answer 1

\(\Leftrightarrow sin^22x+cos^2x=sin^2x+cos^2x\)

\(\Leftrightarrow sin^22x=sin^2x\)

\(\Leftrightarrow4sin^2x.cos^2x=sin^2x\)

\(\Leftrightarrow\left[{}\begin{matrix}sin^2x=0\\4cos^2x=1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}sinx=0\\cosx=\frac{1}{2}\\cosx=-\frac{1}{2}\end{matrix}\right.\)

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

Answer 2

Đề là chúng minh ak bạn