Question

Establish the identity. ln |cot u| = ln |cos u| - ln |sin u| ____________________ Could someone please explain to me how to solve this?

Answer 1

Simply use `ln(a) - ln(b) = ln(a/b)`.

`ln|cotu| = ln|cosu/sinu|`

Now the logarithms cancel out

`cotu = cosu/sinu`

`1/tanu = cosu/sinu`

`1/(sinu/cosu) = cosu/sinu`

`cosu/sinu = cosu/sinu`

Hopefully this helps!