Question

How do you prove `(sin^3x + cos^3x)/sin^3x = cscx/(1-cosx)`?

Answer 1

The equality is not correct.

Explanation:

Let `x = pi/6`:

`(sin^3(pi/6) + cos^3(pi/6))/sin^3(pi/6) = (1/8+(3sqrt(3))/8)/(1/8) = 1+3sqrt(3)`

`csc(pi/6)/(1-cos(pi/6)) = 2/(1-sqrt(3)/2) = 8+4sqrt(3)`