prove that cosA-sinA+1 / cosA+sinA-1 = cosecA+ cotA using the identity cosec^2A= 1+cot^2 A
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(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
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
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