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

(Use the sum of identity for cosine)

Answer 1

The identity in question is

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

so that

cos(a - b) = 12/37 cos(a) + 3/5 sin(b)

Since both a and b lie in the first quadrant, both cos(a) and sin(b) will be positive. Then it follows from the Pythagorean identity,

cos²(x) + sin²(x) = 1,

that

cos(a) = √(1 - sin²(a)) = 4/5

and

sin(b) = √(1 - cos²(b)) = 35/37

So,

cos(a - b) = 12/37 • 4/5 + 3/5 • 35/37 = 153/185