How would you work this out? This is verifying trigonometric equations.
cot^3x+ cotx= cosx(csc^3x)
We don't "work this out"
I believe this is an identity, so we have to prove LeftSide = RightSide
If it is an identiy, if we attempt to "solve" it, we end up 0=0
LS = cot^3 x+ cotx
= cotx(cot^2 x + 1)
= (cosx/sinx)((cos^2 x/sin^2 x + 1)
= (cosx/sinx)(cos^2 x + sin^2 x)/xin^2 x
= (cosx/sinx)(1/sin^2 x)
= cosx/sin^3 x
= cosx csc^3 x
= RS