1/sec(x)-tan(x) = sec(x) + tan(x) I need to verify the trigonometric identity pls

Answer 1

The way you typed it, it is not an identity, you must have meant:

1/(secx - tanx) = secx + tanx

LS = 1/(secx - tanx) *(secx + tanx)/(secx + tanx)
= (secx + tanx)/(sec^2 x - tan^2 x) , but tan^2 x = sec^2 - 1
= (secx + tanx)(sec^2 x - (sec^2 x - 1) )
= (secx + tanx)/1
= RS

Answer 2

clear the fraction. You k ow that
sec^2x = 1 + tan^2x