Question 1131555

{{{(tan(x)+1)^2=(1+2sin(x)* cos(x))/(cos^2(x)) }}}

start with:

{{{(tan(x)+1)^2}}}


={{{tan^2(x)+2tan(x)+1}}}.......{{{tan(x)=sin(x)/cos(x)}}}


={{{sin^2(x)/cos^2(x)+2(sin(x)/cos(x))+1}}}


={{{sin^2(x)/cos^2(x)+2((sin(x)cos^2(x))/cos^2(x))+cos^2(x)/cos^2(x)}}}


={{{(sin^2(x)+2sin(x)cos^2(x)+cos^2(x))/cos^2(x)}}}.......since {{{sin^2(x)+cos^2(x)=1}}}, we have


={{{(1+2sin(x)cos^2(x))/cos^2(x)}}}