Answer:
-480/481
Step-by-step explanation:
In order to use the identity ...
cos(α-β) = cos(α)cos(β) +sin(α)sin(β)
we must find both sine and cosine of the given angles.
sin(α) = 35/37 and α is in quadrant II, so cos(α) = -√(1 -(35/37)^2) = -12/37
cos(β) = 5/13 and β is in quadrant IV, so sin(β) = -√(1 -(5/13)^2) = -12/13
Then the desired cosine is ...
cos(α-β) = (-12/37)(5/13) +(35/37)(-12/13) = -(12·5 +35·12)/(37·13)
cos(α-β) = -480/481
