Give: a=alpha B=beta

Question

csc a= 2
pi/2<a<pi
secB=-3
pi/2<B<pi

1)find sin(a+B)
2)find tan(a-B)
3)cos B/2
4)sin a/2

Answer 1

in QII,

if csc a = 2,
sin a = 1/2
cos a = -√3/2
tan a = -1/√3

if sec B = -3,
cos B = -1/3
sin B = √8/3
tan B = -√8

Now it's just plug and chug, using your sum-of-angles and half-angle formulas. Come on back if you get stuck.