Question

In △ PQR,angle P and angle Q are complementary angles. If sin Q= 4/5 ,cos P+cos Q= .

Answer 1

In triangle PQR, where angles P and Q are complementary, and given sin Q = 4/5, the sum cos P + cos Q is equal to 7/5.

Step-by-step explanation:

If in △ PQR, angle P and angle Q are complementary angles, this means that the sum of their measures is 90 degrees. Given that sin Q = 4/5, to find cos P + cos Q, one can use the trigonometric identity sin2 Q + cos2 Q = 1 and the fact that cos P = sin Q since the angles are complementary.

First, we find cos Q:

cos2 Q = 1 - sin2 Q = 1 - (4/5)2
cos Q = √(1 - 16/25) = √(9/25) = 3/5

Since the angles are complementary, cos P = sin Q = 4/5.

Now, we can find the sum:

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