Prove cosecA (1-cos A) (cosec A + cot A) = 1
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LHS = cosecA (1-cos A) (cosec A + cot A)
= (cosecA-cosecAcosA)(cosecA+cotA)
= (cosecA-cotA)(cosecA+cotA)
[ Since , cosecAcosA = cosA/sinA = cotA ]
= cosec²A - cot²A
= 1
[ Since , cosec²A - cot²A = 1 ]
= RHS
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