evaluate the expression assuming that cos(x)=1/7, sin(y)=1/3, sin(u)=2/5 and cos(v)=1/3. what is cos(u+v)? sin(x-y)? and tan(u-v)?

Answer 1

just plug in you addition formulas:

sin(u+v) = sinu cosv + sinv cosu
= (2/5)(1/3) + (√21/5)(√8/3) = 2(1+√42)/15

do the others likewise. If necessary, draw triangles and label the sides to evaluate the other functions of u,v,x,y