Question

How do you verify `sinx/(1-cosx) - (sinxcosx)/(1+cosx)=cscx(1+cos^2x)`?

Answer 1

We have:

`(sinx(1 +cosx) - sinxcosx(1 - cosx))/((1 - cosx)(1 + cosx)) = cscx(1 + cos^2x)`

`(sinx + sinxcosx - sinxcosx + sinxcos^2x)/((1 - cosx)(1 +cosx)) = cscx(1 +cos^2x)`

`(sinx + sinxcos^2x)/(1 - cos^2x) = cscx(1 + cos^2x)`

`(sinx+ sinxcos^2x)/sin^2x = cscx(1 +cos^2x)`

`(sinx(1 + cos^2x))/sin^2x = cscx(1 +cos^2x)`

`cscx(1 + cos^2x) = cscx(1 + cos^2x)`

As required.

Hopefully this helps!