`(cotg^2 alpha-cos^2 alpha)/(cotg^2 alpha)+(sin alpha.cos alpha)/(cotgalpha)`

`=1-(cos^2 alpha)/(cotg^2 alpha)+(sin alpha.cos alpha)/((cos alpha)/(sin alpha))`

`=1-(cos^2 alpha)/((cos^2 alpha)/(sin^2 alpha))+(sin alpha.cos alpha) . (sin alpha)/(cos alpha)`

`=1-cos^2 alpha . (sin^2 alpha)/(cos^2 alpha)+sin^2 alpha`

`=1-sin^2 alpha+sin^2 alpha`

`=1 (đpcm)`