CotA + cosec A-1 /cot A - cosec A +1 = 1 + cos A /sin A
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Sol:
(Cot A + Cosec A - 1) / (Cot A - Cosec A + 1)
= (Cot A + Cosec A) - (Cosec2 A - Cot2 A) / (Cot A - Cosec A + 1)
= (Cot A + Cosec A) [1 - Cosec A + Cot A) / (Cot A - Cosec A + 1)]
= (Cot A + Cosec A)
= (Cos A/Sin A + 1/Sin A)
= (1 + Cos A) / Sin A
Hence proved.
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