Question 311165
Simplify:

{{{((1+Sinx)/Cosx) + (Cosx/(1+Sinx))}}}

Get the LCD of {{{Cosx(1+Sinx)}}}

 
{{{((1+Sinx)/Cosx)((1+Sinx)/(1+Sinx))+(Cosx/(1+Sinx))(Cosx/Cosx)}}}

{{{(1+2sinx+Sin^2x)/(Cosx(1+Sinx)) + (Cos^2x)/(Cosx(1+Sinx)) }}}

{{{(1+2sinx+Sin^2x + Cos^2x)/(Cosx(1+Sinx)) }}}

Use the identity {{{Sin^2x + Cos^2x = 1}}}

{{{(1+2sinx+1)/(Cosx(1+Sinx)) }}}

{{{(2+2sinx)/(Cosx(1+Sinx)) }}}

{{{(2(1+sinx))/(Cosx(1+Sinx)) }}}

{{{(2(cross(1+sinx)))/(Cosx(cross(1+Sinx))) }}}

{{{2/Cosx}}}

{{{2(1/Cosx)}}}

{{{2Secx}}}

Edwin