solving Natural Logs for x and a Trig identity question.

Hey.

Code:

`2Ln2 - Ln(x-1) = ln(2x)`

That is what im having trouble sorting out. I know its something to do with the quadratic formula but its just not clicking in my head.

also, i cant seem to finish this off:

Code:

`Prove that (1/cot^2 θ) - (1/csc^2 θ) = (sin^4 θ)/(cos^2 θ)`

This is what i have so far:

Code:

`-> (1/(1/tan^2 θ)) - (1/(1/sin^2 θ))`

-> 1/(tan^2 θ - sin^2 θ)

-> (1/((cos^2 θ)/(sin^2 θ))) - (1/sin^2 θ)

-> ((sin^2 θ)/(cos^2 θ)) + ((sin^2 θ)/ 1)

i am stuck there... unless of course the actually DO add together to make

Code:

`(sin^4 θ)/(cos^2 θ)`

Any help would be greatly appreciated!