How do I prove the following identity?

Question

sec^2x-1
(division line)> -------- = (tanx)(secx)
(sinx)

Answer 1

write it this way:

(sec^2 x - 1)/sinx = tanxsecx

In your repertoire of basic trig formulas you should have
sec^2 x = tan^2 + 1

LS= (tan^2 x + 1 - 1)/sinx
= (sin^2 x/cos^2 x)(1/sinx)
= sinx/cos^2 x
= (sinx/cosx) (1/cosx)
= tanx secx
= RS