Find the exact value of the trigonometric expression given t

Find the exact value of the trigonometric expression given that sin u = 3/5 and cos v = 24/25 . (Both u and v are in Quadrant III.) cos(u + v)

Solution

sin u = 3/5 and cos v = 24/25 . (Both u and v are in Quadrant III.)

cosu = -4/5 ; sinv = -7/25

cos(u + v) = cosucosv - sinusinv

= (-4/5)(-24/25) - (-3/5)(-7/25)

= (96 + 21)/125

=117/125