Question 1199276

 {{{cos(x)/(1+sin(x))+(1+sin(x))/cos(x)}}}.............common denominator


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


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


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


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


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


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


={{{2 (1/cos(x))}}}........................{{{1/cos(x)=sec(x)}}}


={{{2 sec(x)}}}