1.
`\frac{1-cosx}{sinx}=sinx/(1+cosx)`
`=>(1-cosx)(1+cosx)=sin^2x`
`<=>1-cos^2x=sin^2x`
`<=>sin^2x+cos^2x=1` (luôn đúng)
Vậy `\frac{1-cosx}{sinx}=sinx/(1+cosx)` $\text{(đpcm)}$
2.
`(1-1/cosx)(1+1/cosx)+tan^2x=0`
`VT=(1-1/cosx)(1+1/cosx)+tan^2x`
`=1-1/cos^2x+tan^2x`
`=1-(1+tan^2x)+tan^2x`
`=0=VP`
Vậy`(1-1/cosx)(1+1/cosx)+tan^2x=0` $\text{(đpcm)}$