Question

prove that _/1+cosA/1-cosA =cosecA+cotA​

Answer 1

Answer:

1+cosA/1-cosA = (cosecA+cotA)² is correct

Step-by-step explanation:

1+cosA/1-cosA

divide on numerator and denominator by sinA

(1+cosA)/sinA÷(1-cosA)/sinA

cosecA+cotA/cosecA-cotA       (∵1/sinA=cosecA and cosA/sinA=cotA)

multiply and divide by (cosecA+cotA)

(cosecA+cotA)(cosecA+cotA)÷(cosecA-cotA)(cosecA+cotA)

(cosecA+cotA)²/cosec²A-cot²A

(cosecA+cotA)²                            (∵ cosec²A-cot²A=1)

∴ 1+cosA/1-cosA = (cosecA+cotA)²

hence proved