Cosa sina 1 cosa sina 1 coseca cota
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Prove that cosA-sinA+1 / cos A+sinA-1 = cosecA+cotA
Answered by admin @
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 ^_^
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