cos A - sin A +1/
cos A +sin A-1=cosecA+cotA
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Answer:
LHS =
(cosA-sinA)+1/(cosA+sinA)-1
Taking conjugate.
(cosA-sinA)+1/(cosA+sinA)-1 × (cosA+sinA)+1/(cosA+sinA)+1
On solving,
=cos2A-sin2A+2cosA+1/2sinAcosA
= cos2A-sin2A+2cosA+sin2A+cos2A/2sinAcosA
= 2cos2A+2cosA/2sinAcosA
= cosA+cos2A/sinAcosA
= cosA/sinAcosA +cos2A/sinAcosA
= cosecA+cotA =R.H.S
Hence, proved.
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