prove:

Question

1+cosx/1-cosx-1-cosx/1+cosx=4cotxcscx

Answer 1

The only way this is true is if
(1+cosx)/(1-cosx) - (1-cosx)/(1+cosx)=4cotxcscx

I will assume you meant to type that

LS
= [(1+cosx)^2 - (1 - cosx)]/(1 - cos^2x)
= [1 + 2cosx + cos^2x - (1 - 2cosx + cos^2x)]/sin^2x
= 4cosx/sin^2x
= 4(cosx/sinx)/sinx
= 4cotxcscx
= RS