Question

How do we simplify `(1 - tanx)/(1 - cotx)`?

Answer 1

We simplify as follows, using the identities `tanx = sinx/cosx` and `cotx = cosx/sinx`.

`=(1 - sinx/cosx)/(1 - cosx/sinx)`

`=((cosx- sinx)/cosx)/((sinx - cosx)/sinx)`

`=(cosx - sinx)/cosx * sinx/(sinx - cosx)`

`=-(sinx - cosx)/cosx * sinx/(sinx - cosx)`

`=-sinx/cosx`

`=-tanx`

Practice Exercises

`1`. Simplify the following.

`(cotx + 1)/(tanx + 1)`

Solution

`=cotx`

Hopefully this helps!