(sec(x) / (sec(x)-1)) - (sec(x) / (sex(x)+1)) = 2cot(x)csc(x)

Answer 1

On the left, get a common denominator of

(secx-1)(secx+1) giving

secx(secx+1)-secx(secx-1) all over the denominator
which reduces to
2secx over the denominator

2secx/(sec^2x-1)=
2secx*cos^2x/(1-cos^2x)=2cosx/sin^2x

=2ctnx/sinx=2ctnx*cscx