Question

cho \(0< \alpha< \frac{3\pi}{2}\) và \(sin\alpha=-\frac{2}{5}\). Tính GTBT \(A=cos2\alpha+tan\alpha\)

Answer 1

\(\left\{{}\begin{matrix}0< a< \frac{3\pi}{2}\\sina< 0\end{matrix}\right.\) \(\Rightarrow\pi< a< \frac{3\pi}{2}\Rightarrow cosa< 0\)

\(\Rightarrow cosa=-\sqrt{1-sin^2a}=-\frac{\sqrt{21}}{5}\Rightarrow tana=\frac{sina}{cosa}=\frac{2\sqrt{21}}{21}\)

\(\Rightarrow A=1-2sin^2a+tana=1-2.\left(-\frac{2}{5}\right)^2+\frac{2\sqrt{21}}{21}=...\)

Answer 2

https://i.imgur.com/YbTKr48.jpg