Đặt \(y=sinx\left(y\in\left[-1;1\right]\right)\).
\(cos\left(sinx\right)=1\)
\(\Leftrightarrow cosy=1\)
\(\Leftrightarrow y=k2\pi\)
Vì \(y\in\left[-1;1\right]\Rightarrow-1\le k2\pi\le1\Leftrightarrow-\dfrac{1}{2\pi}\le k\le\dfrac{1}{2\pi}\)
\(\Rightarrow k=0\)
\(\Rightarrow y=0\)
\(\Leftrightarrow sinx=0\)
\(\Leftrightarrow x=k\pi\)
\(\Leftrightarrow k\in\left\{0;1;2\right\}\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\pi\\x=2\pi\end{matrix}\right.\)
\(\Rightarrow S=3\pi\)