cot² A/cosec A + 1)²=1-sin A/1+sin A.

Answer 1

I noticed that you made a correction from your previous post, but It still would not work.
It should be:

cot² A/(cosec A + 1)²= (1-sin A)/(1+sin A)

notice the important brackets.

LS = cot² A/(cosec A + 1)²
= (cos^2 A/sin^2 A)/(1/sina + 1)^2
= (cos^2 A/sin^2 A)((1 + sinA)^2/sin^2 A)
= (cos^2 A/sin^2 A)*(sin^2 A)/(1 + sinA)^2
= cos^2 A/(1+sinA)^2
= (1-sin^2 A)/(1+sinA)^2
= (1-sinA)(1+sinA)/( (1+sinA)(1+sinA) )
= (1 - sinA)/(1 + sinA)
= RS