Question

If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=3/5and cos b=12/37
1) 153/185

2) 57/185

3) -57/185

4) -153/185

Answer 1

See my answer to your other question for more details (26127939).

We found that cos(a) = 4/5 and sin(b) = 35/37. Then

cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

cos(a + b) = 2/37 • 4/5 - 3/5 • 35/37

cos(a + b) = -57/185

Answer 2

You have to find the cos of angle A, so use the Pythagorean equation and trig laws to find the other side of the triangle created by angle A. 3^2 + x^2 = 5^2. x=4. This means cos(A) = 4/5). Make both cos (A) and cos (B) have equal denominators, and add. 148/185 + 60/185 = 208/185. This answer is correct, though it doesn’t appear to be any of the answers you wrote, so either those answers are wrong or you wrote something incorrectly in the problem.