How do you prove that $cot^3x/cscx = cosx(csc^2x-1)$ ?

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Answer 1 · 2015-05-25T15:28:40

Left side: $cos^3 x/sin^3 x (sin x) = cos^3 x/sin^2 x$ =

= $cos x.((cos^2 x)/(sin^2 x))$ = $cos x[(1 - sin^2 x)/sin^2 x]$ =

= #cos x.(1/sin^2 x - 1) = cos x(csc^2 x - 1)#

How do you prove that cot^3x/cscx = cosx(csc^2x-1)cot^3x/cscx = cosx(csc^2x-1)?