Question

prove that. cosA-sinA+1/cosA+sinA-1=cosecA+cotA

plzzz quick

Answer 1

(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 o
cosA/sinAcosA  +cos2A/sinAcosA

on  solving we get

CosecA+cotA =R.H.S