If $\displaystyle sinA=\frac{2}{\sqrt{5}}$ and $\displaystyle tanB=\frac{1}{2}$, how can I prove that $\displaystyle A-B=45$?

Using a calculator to find inverse sine and tangent then subtracting the angles gets 45 degrees, but I do not think that is the correct way to approach the question.

Similar questions are $\displaystyle sin(A+B+C)=\frac{2\sqrt{2}}{3}$ find $\displaystyle sinC$ etc.

I think when I get the method I should be fine in doing these questions. Thanks!