plz solv this ........
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(cosA - sinA + 1 ) / (cosA + sinA - 1) = cosecA + cot A
divide LHS by (sinA / sinA)
[sinA(cosA - sinA + 1 )] / sinA [(cosA + sinA - 1)]
= (cosA - sinA + 1 )/sinA / (cosA + sinA - 1)/ sinA
= (cotA -1 +cosecA) / ( cotA + 1 - cosecA)
= cotA + cosecA + [cot^2 A - cosec^2 A ] / ( cotA + 1 - cosecA)
= cotA + cosecA + [(cotA+cosecA)(cotA-cosecA) / ( cotA + 1 - cosecA)
= cotA + cosecA { 1 +cotA - cosecA } /( cotA + 1 - cosecA)
= cotA + cosec A
HENCE PROVED
note : in the step 2 : -1 is written as cot^2 A - cosec^2 A by the formula 1+cot^2 A = cosec^2 A
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