Question

How do you verify `1/(secx+1 )= cot^2xsecx-cot^2x`?

Answer 1

We seek to prove that:

`1/(secx+1) -= cot^2x secx-cot^2x`

Consider the RHS:

`RHS = cot^2x secx-cot^2x`

`\ \ \ \ \ \ \ \ = cot^2x(secx-1)`

`\ \ \ \ \ \ \ \ = cot^2x(secx-1) (secx+1)/(secx+1)`

`\ \ \ \ \ \ \ \ = (1/tan^2x(sec^2x-1))/(secx+1)`

`\ \ \ \ \ \ \ \ = (1/tan^2x(tan^2x))/(secx+1)`

`\ \ \ \ \ \ \ \ = (1)/(secx+1)`

`\ \ \ \ \ \ \ \ = LHS \ \ \ \ QED`