Question

Given sin (x-y)=1/4, sin x cos y=3/5,and tan y=3/2,without using mathematical table or scientific calculator,find the values for:
(a)cos x sin y
(b)cos (x+y)

Answer 1

a) sin(x-y) = sinxcosy - cosxsiny
1/4 = 3/5 - cosxsiny
cosxsiny = 3/5 - 1/4 = 7/20

So now we know sinxcosy= 3/5 and cosxsiny = 7/20

form (cosxsiny)/sinxcosy) = (7/20)/(3/5)
cotx tany = 7/12
cotx (3/5) = 7/12
cotx = 35/36
tanx = 36/35

so sinx = 36/√2521
cosx = 35/√2521

from tany = 3/5
siny = 3/√13
cosy = 2/√13

cos(x+y) = cosxcosy - sinxsiny
= (35/√2521)(2/√13) - (36/√2521)(3/√13)

I need somebody to check my arithmetic because if I use my calculator to find the actual angles, I get contradictory results.
I could have made an arithmetic error, (happens lol)

I have a feeling that for the first 2 pieces of information, the third part, namely that tany = 3/5, is not possible.