Question

Tìm max của sin³α + cos³α

Answer 1

Do \(\left|sinx\right|;\left|cosx\right|\le1\Rightarrow\left\{{}\begin{matrix}sin^3x\le sin^2x\\cos^3x\le cos^2x\end{matrix}\right.\)

\(\Rightarrow sin^3x+cos^3x\le sin^2x+cos^2x\)

\(\Rightarrow sin^3x+cos^3x\le1\)

Dấu "=" xảy ra khi \(\left[{}\begin{matrix}sinx=1\\cosx=1\end{matrix}\right.\)