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Answer:
cos A(cosec A - 1 + cosec A + 1)/(cosec^2 A - 1)
=cos A (2cosec A)/cot^2 A
=2cos A * tan^2 A/sinA
=2*cot A*tan A*tan A
= 2tan A(cot A*tan A)
=2 tan A(1)
2 tan A
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