Cho \(\alpha\) là góc nhọn thỏa mãn \(\sin\alpha=\dfrac{5}{13}\). Tính \(\tan\alpha\)
\(\dfrac{12}{13}\)\(\dfrac{12}{5}\)\(\dfrac{5}{12}\)\(\dfrac{13}{5}\)Hướng dẫn giải:Ta có: \(\sin^2\alpha+\cos^2\alpha=1\Rightarrow\cos^2\alpha=1-\left(\dfrac{5}{13}\right)^2=\dfrac{144}{169}\)
Mà \(\alpha< 90^0\Rightarrow0< \cos\alpha< 1\Rightarrow\cos\alpha=\sqrt{\dfrac{144}{169}}=\dfrac{12}{13}\)
\(\Rightarrow\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}=\dfrac{5}{12}\).