Question 927318
{{{cos x+sinx tanx  = cos x + sinx  * (sin x/ cos x)}}}
                   ={{{cos x + (sin x)^2 /cos x}}}
                   =  {{{ cos x + sin^2 (x) / cos x}}}
                    multiply & divide each term with cos x
              ={{{  cos x * (cos x /cos x) +(sin^2 (x) / cos x) *(cos x/cos x)}}}
 ={{{ cos^2(x)/cos x + sin^2(x) /cos x}}}
 = {{{ (cos^2(x)+sin^2(x))/cos x}}}
  But  {{{cos^2(x)+sin^2(x) =1}}}
 = {{{ 1/ cos x}}}
 = sec x
hence proved