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

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Answer 1 · 2016-01-22T00:11:02

The equality is not correct.

Let $x = pi/6$ :

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

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

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