Do \(\left\{{}\begin{matrix}sin\left(x+y\right)\le1\\cos\left(x-y\right)\le1\end{matrix}\right.\) \(\Rightarrow VT\le2\)
Đẳng thức xảy ra khi và chỉ khi:
\(\left\{{}\begin{matrix}sin\left(x+y\right)=1\\cos\left(x-y\right)=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y=\frac{\pi}{2}+k2\pi\\x-y=n2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x=\frac{\pi}{2}+\left(k+n\right)2\pi\\2y=\frac{\pi}{2}+\left(k-n\right)2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{\pi}{4}+\left(k+n\right)\pi\\y=\frac{\pi}{4}+\left(k-n\right)\pi\end{matrix}\right.\)
