Respuesta :

Edufirst
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

In ΔPQR, ∠P and ∠Q are complementary angles. if Sin Q=4/5,COS p+COS Q = 7/5.

What are complementary angles?

Two angles whose sum is 90° are called complementary angles.

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

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

At a right angle:

sec (90-x) = cos (x)

cos (90-x) = sin (x)

Then sin Q = 4/5

cos (90-Q) = cos P = 4/5

Now

[tex]sin^2 (P) + cos^2 (P) = 1[/tex]

[tex]sin^2(P) = 1 - cos^2 (P)\\sin^2(P) = 1 -[4/5]^2 =9/25\\sin(P) = 3/5[/tex]

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

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

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

Learn more about complementary angles here:

https://brainly.com/question/2882938

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