Question

How do you verify `cot^2 x/ (1+csc x) = (1-sin x)/ sin x`?

Answer 1

`sin^2 A + cos^2 A = 1`
Divide by `sin^2 A`
`1 + cot^2 A = csc^2 A`

`cot^2 x/(1+csc x) = (csc^2 x-1)/(1+csc x) = ((csc x-1)(csc x+1))/(1+csc x) = 1/sin x - 1 = (1 - sin x)/sin x`