1/(sec(x)-1)(sec(x)+1)=cot^2(x)

Question

verify the identity 

Answer 1

If I am reading this correctly, you wrote:

1 / [(SecX -1) (SecX + 1)]  = Cot²X    

Verifying trig identities can be a breeze...except when it isn't. This one is, but I admit you'll sometimes see ones needing  a dozen steps or more. Thankfully, not often! Right away, we see a pattern in that left denominator: difference of two perfect squares. If we foil the denominator together, we get:

1 / [Sec²X -1]   = Cot²X

One of your trig identities states that:

Tan²X + 1 = Sec²X

Getting Tan²X alone, we find:

Tan²X = Sec²X - 1

Which we can substitute into your identity:

1 / Tan²X = Cot²X

Cot²X = Cot²X

Answer 2

(sec x - 1)(sec x + 1) = sec² x + 1

Use an identity to continue.