Ta có \(\dfrac{\sin\alpha}{\cos\alpha}=\tan\alpha=2\Rightarrow\sin\alpha=2\cos\alpha\)
Lại có \(\sin^2\alpha+\cos^2\alpha=1\Rightarrow4\cos^2\alpha+\cos^2\alpha=1\)\(\Rightarrow5\cos^2\alpha=1\Rightarrow\cos^2\alpha=\dfrac{1}{5}\Rightarrow\cos\alpha=\dfrac{\sqrt{5}}{5}\)
\(\Rightarrow\sin\alpha=2\cos\alpha=\dfrac{2\sqrt{5}}{5}\)
Ta có:
\(2=tana=\dfrac{sina}{cosa}\Leftrightarrow sina=2cosa\)
\(sin^2a+cos^2a=1\Rightarrow4cos^2a+cos^2a=1\Leftrightarrow cos^2a=\dfrac{1}{5}\Leftrightarrow cosa=\dfrac{\pm\sqrt{5}}{5}\)
- \(cosa=\dfrac{\sqrt{5}}{5}\Rightarrow sina=\dfrac{2\sqrt{5}}{5}\).
- \(cosa=\dfrac{-\sqrt{5}}{5}\Rightarrow sina=\dfrac{-2\sqrt{5}}{5}\).
