Question

cosA-sinA+1/cos A +sinA = cosecA+cotA

Answer 1

Lets take the LHS =

(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

=cosA+cos2A/sinAcosA

we can alsom write in the form of

cosA/sinAcosA  +cos2A/sinAcosA

on  solving we get

CosecA+cotA =R.H.S

I hope it helps you ^_^

Answer 2

Lets take the LHS =

(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

=cosA+cos2A/sinAcosA

we can alsom write in the form of

cosA/sinAcosA  +cos2A/sinAcosA

on  solving we get

CosecA+cotA =R.H.S

I hope it helps you ^_^