Question

If 3sinA+4cosA=5 then find the value of cosA

Answer 1

cos(A) = 4/5

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