Question

prove that,,
[cosecA+cotA-1] / [cotA-cosecA+1] = (1+cosA) /sinA

Answer 1

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.

Answer 2

(cosecA+cotA-1)/(cotA-cosecA+1)

={(cosecA+cotA)-(cosec²A-cot²A)}/(cotA-cosecA+1)

=(cosecA+cotA)(1-cosecA+cotA)/(cotA-cosecA+1)

=cosecA+cotA

=1+cosA/sinA