In ΔPQR, ∠P and ∠Q are complementary angles. if Sin Q=4/5, COS p+COS Q =

P + Q are complementary means that P+Q = 90°.

Then R is a right angle, i. e. it measures 90°.

In a right angle you can write:

sen (90-x) = cos (x)

cos (90-x) = sin (x)

Then sin Q = 4/5 ⇒ cos (90-Q) = cos P = 4/5

Now sin^2 (P) + cos^2 (P) = 1

sin^2 (P) = 1 - cos^2 (P)

sin^2 (P) = 1 - [4/5]^2 = 9/25

sin (P) = 3/5

cos (Q) = sin (P) = 3/5

cos (P) + cos (Q) = 4/5 + 3/5 = 7/5