>>1
= sin (2 csc^(-1) x)
= sin (2 (-i ln(i/x + sqrt(1 - 1/x^2))))
= sin (-2i ln(i/x + sqrt(1-1/x^2)))
= (e^(i(-2i ln(i/x + sqrt(1-1/x^2)))) - e^(-i(-2i ln(i/x + sqrt(1-1/x^2)))))/(2i)
= ((i/x + sqrt(1-1/x^2)) e^2 - (i/x + sqrt(1-1/x^2)) e^(-2))/(2i)
= (i/x + sqrt(1-1/x^2)) (e^2-e^(-2))/(2i)
= (i/x + sqrt(1-1/x^2))/(2i)
= 1/(2x) + sqrt(1-1/x^2)/(2 sqrt(-1))
= 1/(2x) + sqrt((1-1/x^2)/(-1))/2 <----can I do this?
= 1/2 (x + sqrt(1/x^2 - 1))
Is this correct?