Find the exact value of the expression using the provided in

Find the exact value of the expression using the provided information.

Solution

sins = -3sqrt(13)/13 s in in Iv quadrant

tans = -3sqrt13/sqrt52 = -3sqrt(13/52) = -3/2

sint = - sqrt(10)/10 t in IVrt quadrant

tant = -sqrt(10/90) = -1/3

tan(s -t) = [tans - tant]/( 1+tans*tant)

=[ -3/2 +1/3]/[ 1 +1/2]

= (-9 +2)/6 / 3/2

= (-7/6)*(2/3)

= -14/18

= -7/9