Question

Tìm x, biết \(\sin x.\cos x=0,5\) và \(\sin^2x+\cos^2x=1\)

Answer 1

\(\left(sinx+cosx\right)^2=1+2\cdot0.5=2\)

\(\Leftrightarrow2sin^2\left(x+\dfrac{\Pi}{4}\right)=2\)

\(\Leftrightarrow\left[{}\begin{matrix}sin\left(x+\dfrac{\Pi}{4}\right)=1\\sin\left(x+\dfrac{\Pi}{4}\right)=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{\Pi}{4}=\dfrac{\Pi}{2}+k2\Pi\\x+\dfrac{\Pi}{4}=-\dfrac{\Pi}{2}+k2\Pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\Pi}{4}+k2\Pi\\x=-\dfrac{3}{4}\Pi+k2\Pi\end{matrix}\right.\)