[nacero2000]

OK PEOPLE dumb nacero2000 here again...bestow me with ur knowledge

given that 5sin x cos y + 4cos x sin y = 0 and cot x = 2 wot is the value of cot y??

[Fermat]

put one term on one side of the equals sign and keep the other term on the other side.
Then divide one side by the other and see what you've got.

[Jonny W]

It follows from cot(x) = 2 that cos(x) = 2sin(x). So

5sin(x)cos(y) + 8sin(x)sin(y) = 0
sin(x)(5cos(y) + 8sin(y)) = 0
5cos(y) + 8sin(y) = 0 . . . . . because sin(x) is not zero
5cos(y) = -8sin(y) . . . . . if sin(y) were zero then cos(y) would be too; so sin(y) is not zero
cos(y)/sin(y) = -8/5
cot(y) = -8/5