Đáp án+Giải thích các bước giải:

 `a)`

`A=\frac{2cos45^{o}}{\sqrt{2}}+\sqrt{3}tan30^{o}`

Ta có: $\bullet$ `cos45^{o}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}`

          $\bullet$ `tan30^{o}=\frac{sin30^{o}}{cos30^{o}}`

Mà `sin30^{o}=1/2;cos30^{o}=\frac{\sqrt{3}}{2}`

`->tan30^{o}=1/2:\frac{\sqrt{3}}{2}=1/2.\frac{2}{\sqrt{3}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}`

Ta được:

`->A=\frac{2.\frac{\sqrt{2}}{2}}{\sqrt{2}}+\sqrt{3}.\frac{\sqrt{3}}{3}`

`=\frac{\sqrt{2}}{\sqrt{2}}+\frac{\sqrt{3^{2}}}{3}`

`=1+\frac{3}{3}`

`=1+1`

`=2`

Vậy `A=2`

`b)`

`B=\frac{2sin60^{o}}{\sqrt{3}}-cot45^{o}`

Ta có: $\bullet$ `sin60^{o}=\frac{\sqrt{3}}{2}`

         $\bullet$ `cot45^{o}=\frac{1}{tan45^{o}}`

Mà `tan45^{o}=\frac{sin45^{o}}{cos45^{o}}`

`+)` `sin45^{o}=cos45^{o}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}`

`->cot45^{o}=1:\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}`

`=1:1`

`=1`

Ta được:

`->B=\frac{2.\frac{\sqrt{3}}{2}}{\sqrt{3}}-1`

`=\frac{\sqrt{3}}{\sqrt{3}}-1`

`=1-1`

`=0`

Vậy `B=0`.