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Step-by-step explanation:
cos∅ - sin∅ + 1)/(cos∅ + sin∅-1) dividing sin∅ both Numerator
and denominator. = (cos∅/sin∅ - sin∅/sin∅ + 1/sin∅)/(cos∅/sin∅ + sin∅/sin∅ - 1/sin∅) = (cot∅
- 1 + cosec∅)/(cot∅ + 1 - cosec∅) now, put 1 =
cosec²∅ - cot²∅ in numerator = {cot∅ + cosec∅
- (cosec²∅-cot²∅)}/(cot∅-cosec∅ +1) = (cosec∅+cot∅)(1 - cosec∅ + cot∅)/(cot∅-cosec∅+1) =
cosec∅ + cot∅ = RHS Hence
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