prove that cos theta-sin theta+1/cos theta +sin theta -1 =cosec theta +cot theta
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taking theta as A
cosA+1-sinA/cosA+sinA-1 * cosA+1+sinA/cosA+sinA+1
(cosA+1)^2-sin^2A / (cosA+sinA)^2-1
cos^2A+1+2cosA-sin^2A / cos^2A+sin^2A+2sinAcosA-1
2cos^2A+2cosA / 2sinAcosA
cosA+1 / sinA
cosecA+cotA
cosA+1-sinA/cosA+sinA-1 * cosA+1+sinA/cosA+sinA+1
(cosA+1)^2-sin^2A / (cosA+sinA)^2-1
cos^2A+1+2cosA-sin^2A / cos^2A+sin^2A+2sinAcosA-1
2cos^2A+2cosA / 2sinAcosA
cosA+1 / sinA
cosecA+cotA
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