Question

Giải phương trình sau:

Sin ( π sin x ) =1

Answer 1

\(sin\left(\pi sinx\right)=1\Leftrightarrow\pi.sinx=\frac{\pi}{2}+k2\pi\)

\(\Rightarrow sinx=\frac{1}{2}+2k\)

Do \(-1\le sinx\le1\Rightarrow-1\le\frac{1}{2}+2k\le1\)

\(\Rightarrow-\frac{3}{2}\le2k\le\frac{1}{2}\Rightarrow-\frac{3}{4}\le k\le\frac{1}{4}\Rightarrow k=0\)

\(\Rightarrow sinx=\frac{1}{2}\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{6}+k2\pi\\x=\frac{5\pi}{6}+k2\pi\end{matrix}\right.\)