Question

If sinxsiny=1/4 and 3tanx=4tany , then prove that sin(x+y)=7/16
(wrong question)

Answer 1

sinxsiny=1/4 ..i
3tanx=4tany ....ii
=4tany=3tanx ...iii
Dividing i by ii,
cosx siny/3 = cosy/16siny
siny cosx =3cosy /16siny ....iv
Dividing i by iii,
cosysinx/4 = cosx/12sinx
sinx cosy =cosx /3 siny.....v

Answer 2

sin(x+y) = sinx cosy + sinycosx =cosx/3sinx + 3cosy/16siny
=1/3tanx + 3/16tany
=1/3tanx + 3/4(3tanx)
=1/3tanx + 1/4tanx
=7/12tanx

Answer 3

sin(x+y)=7/16tany

Answer 4

This is not going to happen
If sinxsiny=1/4 and 3tanx=4tany , then prove that sin(x+y)=7/16

you can solve numerically to find sin(x+y) = 0.870460525 which is close to
0.875 = 7/8

Answer 5

you can use trig substitutions and algebra to find angles x and y