#### Answer

cos α = $\frac{sqrt of 2}{sqrt of 3}$ , cos β = $\frac{sqrt of 3}{sqrt of 5}$

#### Work Step by Step

Step 1: By Pythagoras theorem
$(sqrt of 3)^{2}$ + $(sqrt of 2)^{2}$ = $c^{2}$
3 + 2 = $c^{2}$
c = $\sqrt 5$
Step 2:
cos α = $\frac{length of adjacent}{length of hypotenuse}$
cos α = $\frac{sqrt of 2}{sqrt of 3}$
Similarly cos β = $\frac{length of adjacent}{length of hypotenuse}$
cos β = $\frac{sqrt of 3}{sqrt of 5}$
Therefore cos α = $\frac{sqrt of 2}{sqrt of 3}$ , cos β = $\frac{sqrt of 3}{sqrt of 5}$