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QUESTION

How do you prove ##(1+sinx)/(1-sinx)=(secx+tanx)^2##?

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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