Question 1155883
{{{(sec(x) + csc(x))/(1 + tan(x))}}}



use identities:

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

{{{csc(x)=1/sin(x)}}}

{{{tan(x)=sin(x)/cos(x)}}}

then, you have


{{{(sec(x) + csc(x))/(1 + tan(x))}}}


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


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


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


={{{(cos(x)cross((sin(x)+ cos(x))))/((sin(x)cos(x)*cross((cos(x)+sin(x)))))}}}



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


={{{cross(cos(x))/(sin(x)cross(cos(x)))}}}


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


={{{csc(x)}}}