Is this a proof?
(tan x +cot x)/tan x = csc^2 x
\(\begin{align}\\ LHS&=(tanx+cotx)\div tanx\\ &=(\frac{sinx}{cosx}+\frac{cosx}{sinx})\times \frac{cosx}{sinx}\\ &=\frac{sin^2x+cos^2x}{sinxcosx}\times \frac{cosx}{sinx}\\ &=\frac{1}{sinx}\times \frac{1}{sinx}\\ &=\frac{1}{sin^2x}\\ &=csc^2x\\ &=RHS \end{align}\)