Question

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

Answer 1

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)`