Question

How do you prove `(cosA - cotA) / ( 1 - sinA) = - cotA`?

Answer 1

Try this:

Answer 2

Use that `cotA={cosA}/{sinA}` in the left hand side and then factor the expression.

`{cosA-cotA}/{1-sinA}={cosA-{cosA}/{sinA}}/{1-sinA}=cosA({1-1/{sinA}}/{1-sinA})`

`={cosA}/{sinA}((sinA-1}/{1-sinA})={cosA}/{sinA}*(-1)=-cotA`