Question

prove that :
(tan x + sec x - 1)/(tan x - sec x + 1)= (1+sin x)/cos x

Answer 1

tanx+secx−1tanx−secx+1tan⁡x+sec⁡x−1tan⁡x−sec⁡x+1

=sc+1c−ccsc−1c+cc=sc+1c−ccsc−1c+cc

=s+1−cs−1+c=s+1−cs−1+c

=(s−c+1s+c−1)(s+c+1s+c+1)=(s−c+1s+c−1)(s+c+1s+c+1)

=s2−c2+s+c+(s−c)+1s2+c2+2sc−1=s2−c2+s+c+(s−c)+1s2+c2+2sc−1

=s2−(1−s2)+2s+11+2sc−1=s2−(1−s2)+2s+11+2sc−1

=2s2+2s2sc=2s2+2s2sc

=s+1c=s+1c

=1+sinxcosx