Question

P.T.(1 + cosec A). (1 + cos A). (1 - cosec A). (1 - sec A) = cos A​

Answer 1

Answer:

Step-by-step explanation:

cosec A = 1/sin A

(cosec A - 1)/(cosec A + 1) = (1 - sin A)/(1 + sin A) -----------> 1

multiply numerator and denominator in 1 by (1 + sin A) to get

(1 -  sin A)/(1 + sin A) * (1 + sin A)/(1 + sin A) =

(1 - sin^2 A)/1 + sin^2 A) --------------> 2

now 1 - sin^2 A = cos^2 A --------------> standard identity cos^2 A + sin^2 A = 1

so we get from 2 the expression simplified as cos^2 A/(1 + sin A)^2  =

(cos A/(1 + sin A))^2