sin(a+b) = sinacosb +cosasinb = 3/4 (1)
sin(a-b) = sinacosb -cosasinb = 1/2 (2) or - sinacosb+cosasinb= -1/2 (3)
add (1) and (2) together: 2 sina cosb = 5/4 re-arrange sina cosb = 5/8 (4)
add (1) and (3) together 2 cosasinb = 1/4 rearrange cosa sinb = 1/8 (5)
tana /tanb = sina/cosa / sinb/cosb
= sina cosb / cosa sinb sub in (4) and (5)
= 5/8 / 1/8 = 5