Question 1206147
{{{(tan(x) +1)^2* cos(x)}}}

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


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


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


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


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


={{{(sin^2(x) + cos^2(x) + 2sin(x) *cos(x))/cos(x)}}}...use identity {{{sin^2(x) + cos^2(x)=1}}}


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


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


={{{1/cos(x) + 2sin(x)}}} ...use identity {{{1/cos(x)=sec(x)}}}


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