Write an expression for csc2x in terms of cscx. ?

Answer 1

csc(x) = 1/sin(x)

cos(x)^2 + sin(x)^2 = 1

sin(2x) = 2sin(x)cos(x)

csc(2x) =>

1/sin(2x) =>

1/(2 * sin(x) * cos(x)) =>

1/(2 * sin(x) * sqrt(1 - sin(x)^2)) =>

1/(2 * sin(x) * sin(x) * sqrt(csc(x)^2 - 1)) =>

(1/2) * csc(x)^2 * (csc(x)^2 - 1)^(-1/2)