Angle α lies in quadrant II , and tanα=−12/5 . Angle β lies in quadrant IV , and cosβ=3/5 . What is the exact value of cos(α−β) ?

ocmaz Apr 1, 2020

#1**+1 **

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

Since tan(a) = -12/5 and is in quadrant II, sin(a) = 12/13 and cos(a) = -5/13

(It's a 5-12-13 right triangle, with x-value negative and y-value positive.)

Since cos(b) = 3/5 and is in quadrant IV, sin(b) = -4/5.

(It's a 3-4-5 right triangle, with x-value positive and y-value negative.)

Place these values into the formula to get your answer.

geno3141 Apr 1, 2020