1. In right triangle ABC with right angle C , sinA=4/5 and cosA=3/5 . What is sinB+cosB ?
A. 35/12
B. 5/7
C. 7/5
D. 1/5
First, we need to find sinB and cosB using the given information.
Using the Pythagorean theorem, we know that sin^2(A) + cos^2(A) = 1, so:
(4/5)^2 + (3/5)^2 = 16/25 + 9/25 = 25/25 = 1
Since sin^2(B) + cos^2(B) = 1, we know that sinB = sqrt(1 - cos^2(B)) and cosB = sqrt(1 - sin^2(B))
sinB = sqrt(1 - 9/25) = sqrt(16/25) = 4/5
cosB = sqrt(1 - 16/25) = sqrt(9/25) = 3/5
Therefore, sinB + cosB = 4/5 + 3/5 = 7/5
So, the answer is C. 7/5.