Question 978218
{{{2tan x/(1+sec x)+ 2+2sec x/(tan x) }}}
= {{{(2sinx/cosx)/(1+1/cosx) + 2 + (2/cosx)/(sinx/cosx)}}}
= {{{2sinx/(cosx+1)+ 2 +2/sinx}}}
= {{{2sinx(1-cosx)/sin^2(x) + 2 + 2/sinx}}}  (Rationalizing 1st term)
= {{{(2sinx - 2 sinx*cosx +2sin^2(x)+2sinx)/sin^2(x)}}}
= {{{(2sin^2(x)+4sinx-2sinx*cosx)/sin^2(x)}}}
= {{{ 2 + 2(2-cosx)/sinx}}}