Simplify $(tanx+secx-1)/(tanx-secx+1)$ ?

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Answer 1 · 2016-04-29T10:18:28

Please see the proof below.

$(tanx+secx-1)/(tanx-secx+1)$

Multiplying numerator and denominator by $tanx+secx+1$

= $(tanx+secx-1)/(tanx-secx+1)xx(tanx+secx+1)/(tanx+secx+1)$

= $(tan^2x+tanxsecx+tanx+tanxsecx+sec^2x+secx-tanx-secx-1)/(tan^2x+tanxsecx+tanx-tanxsecx-sec^2x-secx+tanx+secx+1)$

= $(tan^2x+2tanxsecx+sec^2x-1)/(tan^2x+2tanx-sec^2x+1)$

As $sec^2x=tan^2x+1$ , above is equal to

= $(tan^2x+2tanxsecx+tan^2x+1-1)/(tan^2x+2tanx-tan^2x-1+1)$

= $(2tan^2x+2tanxsecx)/(2tanx)$

= $(2tanx(tanx+secx))/(2tanx)$

= $tanx+secx$

Simplify (tanx+secx-1)/(tanx-secx+1)(tanx+secx-1)/(tanx-secx+1)?