Find the exact value of the trigonometric function given tha

Find the exact value of the trigonometric function given that sin u = 20/29 and cos v = 3/5 . (Both u and v are in Quadrant III.) sec(v u)

Solution

sin u = 20/29 and cos v = 3/5 . (Both u and v are in Quadrant III.)

cosu = - 21/29 ; sinv = -4/5

sec(v u) = 1/cos(v -u)

cos(v -u) = cosv cosu +sinv sinu

=(-21/29)(-3/5) + (-4/5)(-20/29)

= 143/145

sec(v - u) = 145/143