Question

Prove the trigonometric identity:
(csc^2x)/(cotx)=cscxsecx ...?

Answer 1

cscx = 1 / sinx, so csc^2x = 1/ sin²x, and cotx=cosx / sinx
so (csc^2x)/(cotx)=(1/ sin²x) (sinx/cosx) = 1/(sinxcosx) = 1/sinx 1/cosx
finally
(csc^2x)/(cotx)=cscxsecx