Question 976140
Start with the more complicated expression and simplify.  


{{{1/cosA+sinA+1+1/cosA+sinA-1}}}



You have obvious other simplifications to do first.
{{{1/cos(A)+sin(A)+sin(A)+1/cos(A)+1-1}}}, based on Commutative Property for Addition


{{{2/cos(A)+2sin(A)+0}}}


{{{2/cos(A)+2sin(A)}}}


Simplest common denominator is cos(A).


{{{2/cos(A)+(2sin(A)*cos(A))/cos(A)}}}


{{{highlight_green((2+2sin(A)cos(A))/cos(A))}}}
This appears not to be same as cosec(A)+sec(A).


Try starting with the other expression instead.
{{{csc(A)+sec(A)}}}
{{{1/sin(A)+1/cos(A)}}}
{{{cos(A)/(sin(A)cos(A))+sin(A)/(sin(A)cos(A))}}}
{{{highlight_green((cos(A)+sin(A))/(sin(A)cos(A)))}}}


Much work done so far, but the identity is not proved, and it is likely not an identity.