#(tan x+sec x -1)/(tan x -sec x +1 ) =tan x+ sec x# ?

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Answer 1 · 2018-05-23T12:09:24

#LHS=(tan x+sec x -1)/(tan x -sec x +1 )#

#=(tan x+sec x -(sec^2x-tan^2x))/(tan x -sec x +1 )#

#=((tan x+sec x)(1-secx+tanx))/(tan x -sec x +1 )#

#=tan x+ sec x=RHS#

Answer 2 · 2018-05-23T17:19:23

In the explanation section.

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

=#((tanx+secx-1)(tanx+secx+1))/((tanx-secx+1)(tanx+secx+1))#

=#((tanx+secx)^2-1)/((tanx+1)^2-(secx)^2)#

=#((tanx)^2+2tanx*secx+(secx)^2-1)/((tanx)^2+2tanx+1-(secx)^2)#

=#((tanx)^2+2tanx*secx+(tanx)^2)/((secx)^2+2tanx-(secx)^2)#

=#(2tanx*secx+2(tanx)^2)/(2tanx)#

=#(2tanx*(secx+tanx))/(2tanx)#

=#secx+tanx#