Answer:
cos(A) = 4/5
Step-by-step explanation:
3sinA+4cosA=5
Divide by 5 on both sides
(3/5)sinA+(4/5)cosA = 1 .................(1)
from which sin(A) = 3/5, cos(A) = 4/5 by inspection, since
(3/5)^2+(4/5)^2 = 1
For more details,
Let
cos(B) = (3/5), then
sin(B) = (4/5)
Substitute in (1)
cos(B)sin(A) + sin(B)cos(A) = 1 substitute trigonometric sum
sin(A+B) = 1 => A & B are complementary
cos(A) = sin(B) = 4/5
