Question

How do you simplify `(1+cosx)(cscx-cotx)`?

Answer 1

You can write it as:
`(1+cos(x))(1/sin(x)-cos(x)/sin(x))=`
`(1+cos(x))(1-cos(x))/sin(x)=`
`=(1-cos^2(x))/sin(x)=sin^2(x)/sin(x)=sin(x)`