Giải thích các bước giải:
`a) cot^2\alpha-cos^2\alpha=cot^2\alpha.cos^2\alpha`
Ta có: `cot^2\alpha-cos^2\alpha`
`=``(\frac{cos\alpha}{sin\alpha})^2``- cos^2\alpha`
`=``\frac{cos^2\alpha}{sin^2\alpha}``-cos^2\alpha`
`= cos^2\alpha``(\frac{1}{sin^2\alpha}-1)`
`=cos^2\alpha.``\frac{1-sin^2\alpha}{sin^2\alpha}`
`= cos^2\alpha.``\frac{cos^2\alpha}{sin^2\alpha}`
`=cos^2\alpha``(\frac{cos\alpha}{sin\alpha})^2``= cos^2\alpha.cot^2\alpha`
`b)``\frac{1+cos\alpha}{sin\alpha}``=``\frac{sin\alpha}{1-cos\alpha}`
Ta có: `\frac{1+cos\alpha}{sin\alpha}``=``\frac{(1+cosalpha)(1-cosalpha)}{sinalpha(1-cosalpha)}``=``\frac{1-cos^2}{sinalpha(1-cosalpha)}``=``\frac{sin^2alpha}{sinalpha(1-cosalpha)}``=``\frac{sin^2alpha}{1-cosalpha}`
