#\frac{\sin\alpha}{\cos\alpha}=\tg\alpha#
#\frac{\sin\alpha}{\cos\alpha}=\frac{2}{3}#
#\sin ^2\alpha + \cos ^2\alpha =1#
#\cos\alpha = \sqrt{1-\sin ^2\alpha} #
#\frac{\sin\alpha}{\sqrt{1-\sin ^2\alpha}}=\frac{2}{3}#
#\frac{\sin\alpha}{\sqrt{(1+\sin\alpha )(1- \sin\alpha)}}=\frac{2}{3}#
#\frac{sin ^2\alpha}{(1+\sin\alpha )(1- \sin\alpha)}=\frac{4}{9}#
#9sin^2\alpha=4(1+\sin\alpha )(1- \sin\alpha)#
#9sin^2\alpha=4(1-sin^2\alpha)#
#9sin^2\alpha=4-4sin^2\alpha#
#13sin^2\alpha=4#
#sin\alpha = \pm\sqrt{\frac{4}{13}}#
#\text{If we check the solutions, when} \
a=-\sqrt{frac{4}{13}}\text{ the equation doesn't hold true , so the solution is} sin\alpha=\frac{2}{\sqrt{13}}#
#cos\alpha=\sqrt{1-(\frac{2}{\sqrt{13}})^2}=\frac{3}{\sqrt{13}#
