(cosecA-cotA+1)/(cosecA+cotA+1)
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cosecA-cotA+1/cosecA+cotA+1
=(cosecA-cotA)+(cosec²A-cot²A)/cosecA+cotA+1
=(cosecA-cotA)(1+cosecA+cotA)/cosecA+cotA+1
=cosecA-cotA
=(1-cosA)/sinA
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