Fill in the blank to complete the trigonometric formula cos

Fill in the blank to complete the trigonometric formula. cos u - cos v = Use the figure to find the exact value of the trigonometric function. sin theta/2 =

Solution

1) cosu - cosv

use the formula : cosx - cosy = -2sin(x+y)/2sin(x -y)/2

cosu - cosv = -2sin(u+v)/2sin(u-v)/2

2) secthet/2 = 1/cos(theta/2)

costheta = 35/37

cos(theta/2) = sqrt[(1+costheta)/2]

= sqrt[ (1+ 35/37)/2]

= sqrt(72/2*37)

= sqrt(36/37)

= 6/sqrt(37)

sec(theta/2) = sqrt37/6

= sqrt[