Question

cos A - sin A + 1 / cos A + sin A - 1 = cosec A + cotA

Answer 1

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

(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