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