So think of a triangle (draw this out of you need to). So sine = opposite over hypotenuse
And cosine = adjacent over hypotenuse
So the sin of angle Q is 4/5 meaning the hypotenuse is 5 and the opposite side to that angle is 4. Use the Pythagorean theorem to solve for the adjacent side
a^2+b^2=c^2
a^2+16=25
a^2=9
So a= 3
So the side lengths are 4 and 3 and the hypotenuse is 5. Now solve for the cosine of angles P and Q and add those fractions together. If you need further help let me know and I can work it out with you!