`a)A=1/(tan\alpha+1)+1/(cot\alpha+1)`

`=(cot\alpha+1+tan\alpha+1)/((tan\alpha+1)(cot\alpha+1))`

`=(cot\alpha+tan\alpha+2)/(tan\alpha*cot\alpha+tan\alpha+cot\alpha+1)`

`=(cot\alpha+tan\alpha+2)/(1+tan\alpha+cot\alpha+1)`

`=(cot\alpha+tan\alpha+2)/(cot\alpha+tan\alpha+2)`

`=1`

Vậy: `A=1`

`b)B=cos(pi/2-\alpha)-sin(pi+\alpha)` 

`=sin\alpha-(-sin\alpha)`

`=sin\alpha+sin\alpha`

`=2sin\alpha`

`c)C=sin(\alpha-pi/2)+cos(-\alpha+6pi)-tan(\alpha+pi)*cot(3pi+\alpha)`

`=(-cos\alpha)+cos(-\alpha)-tan\alpha*cot\alpha`

`=-cos\alpha+cos\alpha-1`

`=0-1`

`=-1`

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Công thức:

`@tan\alpha*cot\alpha=1`

`@cos(pi/2-\alpha)=sin\alpha`

`@sin(pi+\alpha)=-sin\alpha`

`@sin(\alpha-pi/2)=-cos\alpha`

`@cos(\alpha+k2pi)=cos\alpha`

`@cos(-\alpha)=cos\alpha`

`@tan(\alpha+pi)=tan\alpha`

`@cot(kpi+\alpha)=cot\alpha`