Find the exact value of each expression using additoin and s

Find the exact value of each expression using additoin and subtraction formulas, double angle formulas, and or half angle formulas.

Given: csc x= -4/3, x in quadrant 3 and tan y=5/12, y in quadrant 1

Find:

cos(x-y)

sin(2x)

tan(y/2)

x in quadrant 3

csc x= -4/3=>sinx =-3/4

cosx = -(4²-3²) /4 =-(7)/4

y in quadrant 1

tan y=5/12

sin y =5/[5²+12²] =5/13

cos y =12/[5²+12²] =12/13

cos(x-y)=cosxcosy +sinxsiny

cos(x-y)=(-(7)/4)(12/13) +(-3/4)(5/13)

cos(x-y)=(-(127) -15)/13

sin(2x) =2sinxcosx

sin(2x)=2(-3/4)(-(7)/4)

sin(2x)=3(7)/8

tan(y/2) =[(1-cosy)/(1+cosy)]

tan(y/2) =[(1-(12/13))/(1+(12/13))]

tan(y/2) =1/5