In ΔPQR, ∠P and ∠Q are complimentary angles. If sinQ = 4/5, cosP + cosQ =

Complimentary means

P + Q = 90

P = 90 - Q

Cos (p) = cos (90-Q) = sinQ = 4/5 (given)

You can find CosQ from the triangle of Q

CosQ = sqrt (5^2 - 4^2) / 5 = 3/5

Required = CosP + CosQ = 4/5 + 3/5 = 7/5