How do you prove ##(1+sinx)/(1-sinx)=(secx+tanx)^2##?
February 20th, 2023
see below
##(1+sinx)/(1-sinx)=(secx+tanx)^2##
Right Side ##=(secx+tanx)^2##
##=(secx+tanx)(secx+tanx)##
##=sec^2x+2secxtanx+tan^2x##
##=1/cos^2x +2*1/cosx *sinx/cosx +sin^2x/cos^2x##
##=(1+2sinx+sin^2x)/cos^2x##
##=((1+sinx)(1+sinx))/(1-sin^2x)##
##=((1+sinx)(1+sinx))/((1+sinx)(1-sinx))##
##=(1+sinx)/(1-sinx##
##=## Left Side
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