Question

COS A Sin A+1/COS A+ Sin A-1= 1/CotA-CosecA​

Answer 1

Answer:

(cos A- sin A + 1)/(cos A + sin A - 1). Divide both numerator and the denominator by sinA.the sum becomes

(cot A - 1 + cosec A)/(cot A + 1 -cosec A)

=(cosec A + cot A - 1)/(cotA - cosec A +1)

={cosecA+cotA-(cosec^2 A- cot^2 A)}/Dr where Dr=cotA-cosecA+1

={(cosecA+cotA)-(cosecA+cotA)(cosecA-cotA)}/ Dr.

=[(cosecA+cotA){1-(cosecA-cotA)}]/Dr

={(cosecA+cotA)(1-cosecA+cotA)}/Dr

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

=(cosecA+cotA).Dr/Dr

=cosecA+cotA.