`sqrt2.sinalpha-2cosalpha=0`

`<=>sinalpha=(2)/(sqrt2).cosalpha`

Áp dụng : `sin^(2)alpha+cos^(2)alpha=1`

`=>(2/(sqrt2)).cosalpha)^2+cos^(2)alpha=1`

`<=>(1)/(2).cos^(2)alpha+cos^(2)alpha=1`

`<=>3/(2).cos^(2)alpha=1`

`<=>cos alpha=-sqrt(2/3)` Vì `90^(o)<alpha<180^o`

`=>sin alpha=(2)/(sqrt2).cos alpha=(-2sqrt3)/3`

`=>cot alpha=-sqrt2/2`

`2)` 

Ta có : `A=(cot a-tana)/(tana+2cota)`

`=(cos^(2)a-sin^(2)a)/(sina.cosa):(sin^(2)a+2cos^(2)a)/(sina.cosa)`

`=(cos^(2)a-sin^(2)a)/(sin^(2)a+2cos^(2)a)`

`=(1-2sin^(2)a)/(1+(1-sin^(2)a))`

`=(1-2sin^(2)a)/(2-sin^(2)a)`

`=(1-2.(1/3)^2)/(2-(1/3)^2)`

`=7/17`