Question

How do you factor and simplify `secxcscx-csc^2x`?

Answer 1

Factor out a `cscx`:

`=>cscx(secx - cscx)`

Simplify using the reciprocal identities `csctheta = 1/sintheta` and `sectheta = 1/costheta`.

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

`=> 1/(sinxcosx) - 1/(sin^2x)`

`=> sinx/(sin^2xcosx) - cosx/(sin^2xcosx)`

`=>(sinx - cosx)/(sin^2xcosx)`

`=>csc^2xsecx(sinx - cosx)`

This is as far as we can go. It should be noted that `x !=2pin, pi/2 + 2pin`

Hopefully this helps!