Đáp án:
$P=\dfrac{24}{25}$
Giải thích các bước giải:
$\dfrac{\pi}{2}<\alpha<\pi⇒\begin{cases}\sin\alpha>0\\\cos\alpha<0\end{cases}$
$\sin\alpha=\dfrac{4}{5}$
Ta có:
$\sin^2\alpha+\cos^2\alpha=1$
$⇒\cos^2\alpha=1-\sin^2\alpha$
$⇒\cos\alpha=-\sqrt{1-\sin^2\alpha}=-\sqrt{1-\left(\dfrac{4}{5}\right)^2}=-\dfrac{3}{5}$
$⇒P=\sin(2\alpha+\pi)=-\sin2\alpha=-2\sin\alpha\cos\alpha=-2.\dfrac{4}{5}.\left(-\dfrac{3}{5}\right)=\dfrac{24}{25}$.
