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

1 Answer
Apr 29, 2016

Please see the proof below.

Explanation:

#(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#