Prove the identity: tanx / secx + 1 = secx - 1 / tanxShow all steps so that Left Side = Right Side

Expert Answers
embizze eNotes educator| Certified Educator

Show `(tanx)/(secx+1)=(secx-1)/tanx` :

`(tanx)/(secx+1)`

`=tanx/(secx+1)*(secx-1)/(secx-1)`  Multiplying by 1

`=(tanx(secx-1))/(sec^2x-1)`

`=(tanx(secx-1))/(tan^2x)`  Pythagorean identity

`=(secx-1)/tanx` as required.