Question

How do you find the exact value of `tan(u-v)` given that `sinu=-7/25` and `cosv=-4/5`?

Answer 1

`tan(u-v)=-1/3`

Explanation:

we have `sinu=-7/25` `cosv=-4/5` as the negative signs indicate the quadrants which these angles belong to we can place the signs at last.

from the figures we can say that
`tanu=7/24`, `tanv=3/4`
required`:` `tan(u-v)=[(tanu-tanv)/(1+tanutanv)]` substituting the values we get
`tan(u-v)=(7/24-3/4)/(1+3/24.(3/4)]=((7-18)/24)/(1+3/24)=-9/27=-1/3`
`:.tan(u-v)=-1/3`