Chứng minh hệ thức : `cot^2 a-cos^2 a =cotg^2 a . cos^2 a`

Ta có: `VT = cot^2 \alpha - cos^2 \alpha`

`= ((cos\alpha)/(sin\alpha))^2 - cos^2 \alpha` (do`cot\alpha = (cos\alpha)/(sin\alpha)`)

`= (cos^2 \alpha)/(sin^2 \alpha) - cos^2 \alpha`

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

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

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

`= (cos^2 \alpha)/(sin^2 \alpha) . cos^2 \alpha`

`= ((cos \alpha)/(sin\alpha))^2 . cos^2 \alpha`

`= cotg^2 \alpha . cos^2 \alpha` (do `(cos \alpha)/(sin \alpha) = cotg \alpha`) `= VP` (đpcm)

`@`Duongg7109612009