CosA-SinA+1/CosA+SinA-1=CosecA+CotA

(cosA-sinA)+1/(cosA+sinA)-1

taking conjugate

(cosA-sinA)+1/(cosA+sinA)-1  *  (cosA+sinA)+1/(cosA+sinA)+1

multiplying we get

=cos²A-sin²A+2cosA+1/2sinAcosA

=cos²A-sin²A+2cosA+sin²A+cos²A/2sinAcosA                  

on solving we get

=2cos²A+2cosA/2sinAcosA

=taking 2 common and divided

we get

=cosA+cos²A/sinAcosA

we can alsom write in the form of

cosA/sinAcosA  +cos²A/sinAcosA

on  solving we get

CosecA+cotA =R.H.S

by swapnil sudhir