1)tan alpha=2(0<alpha<90).Tính sin alpha,cos alpha. 2)cos alpha=3/5.Tính sin alpha,tan alpha. 3)tan alpha=3.Tính A =3sin alpha-cos alpha/sin alpha+cos alpha.

Ta có:
$\displaystyle 1+\tan^{2} \alpha =\frac{1}{\cos^{2} \alpha }$
$\displaystyle \Leftrightarrow 1+2^{2} =\frac{1}{\cos^{2} \alpha }$
$\displaystyle \Leftrightarrow 5=\frac{1}{\cos^{2} \alpha }$
$\displaystyle \Leftrightarrow 5\cos^{2} \alpha =1$
$\displaystyle \Leftrightarrow \cos^{2} \alpha =\frac{1}{5}$
$\displaystyle \Leftrightarrow \cos \alpha =\pm \frac{1}{\sqrt{5}}$
+) Với $\displaystyle \cos \alpha =\frac{1}{\sqrt{5}}$
$ $Ta có:
$\displaystyle \tan \alpha =\frac{\sin \alpha }{\cos \alpha }$
$\displaystyle \Rightarrow \sin \alpha =\tan \alpha \cos \alpha $
$\displaystyle \Rightarrow \sin \alpha =\frac{2\sqrt{5}}{5}$
+) Với $\displaystyle \cos \alpha =-\frac{1}{\sqrt{5}}$
$\displaystyle \Rightarrow \sin \alpha =\tan \alpha \cos \alpha $
$\displaystyle \Rightarrow \sin \alpha =2.\left(\frac{-1}{\sqrt{5}}\right)$
$\displaystyle \Rightarrow \sin \alpha =\frac{-2\sqrt{5}}{5}$