Question

COS A-Sin A +1÷Cos A +Sin A - I = C0Sec A +Cot A

Answer 1

Cos A - Sin A + 1/ Cos A + Sin A - 1 dividing in numerator & denominator with Sin A
Cot A - 1 + Cosec A / Cot A - Cosec A + 1
now putting 1= Cosec^2 - Cot ^2

= (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) RHS Proved