#[1]" "(1+sinx)/(1-sinx)-(1-sinx)/(1+sinx)#
Combine the two terms by making them have the same denominator.
#[2]" "=((1+sinx)/(1-sinx))((1+sinx)/(1+sinx))-((1-sinx)/(1+sinx))((1-sinx)/(1-sinx))#
#[3]" "=(1+2sinx+sin^2x)/(1-sin^2x)-(1-2sinx+sin^2x)/(1-sin^2x)#
#[4]" "=(1+2sinx+sin^2x-1+2sinx-sin^2x)/(1-sin^2x)#
#[5]" "=(4sinx)/(1-sin^2x)#
Pythagorean Identity: #1-sin^2theta=cos^2theta#
#[6]" "=(4sinx)/(cos^2x)#
#[7]" "=(4sinx)/((cosx)(cosx))#
Quotient Identity: #sintheta/costheta=tantheta#
#[8]" "=(4tanx)/(cosx)#
Reciprocal Identity: #1/costheta=sectheta#
#[9]" "=4tanxsecx#
#color(blue)("":.(1+sinx)/(1-sinx)-(1-sinx)/(1+sinx)=4tanxsecx)#