`a)` `cos ((3pi)/2+alpha)=cos((3pi)/2).cos alpha - sin((3pi)/2).sin alpha`

`= 0.cos alpha - (-1).sin alpha`

`= sin alpha`

`b)` `sin((5pi)/2+alpha)=sin((5pi)/2).cos alpha + cos((5pi)/2).sin alpha`

`=1.cos alpha + 0.sin alpha`

`= cos alpha`

`c)` Ta xét các giá trị lượng giác:

`@ sin((7pi)/2+alpha)=sin((7pi)/2).cos alpha + cos((7pi)/2).sin alpha`

`=-1.cos alpha + 0.sin alpha`

`= -cos alpha`

`@ cos ((7pi)/2+alpha)=cos((7pi)/2).cos alpha - sin((7pi)/2).sin alpha`

`= 0.cos alpha - (-1).sin alpha`

`= sin alpha`

`=>` $\tan (\dfrac{7\pi}{2}+ \alpha)=\dfrac{\sin (\dfrac{7\pi}{2}+\alpha)}{\cos (\dfrac{7\pi}{2}+\alpha)}$

`=(-cos alpha)/(sin alpha)=-cot alpha`

`d)` Ta xét các giá trị lượng giác:

`@ sin((9pi)/2+alpha)=sin((9pi)/2).cos alpha + cos((9pi)/2).sin alpha`

`=1.cos alpha + 0.sin alpha`

`= cos alpha`

`@ cos ((9pi)/2+alpha)=cos((9pi)/2).cos alpha - sin((9pi)/2).sin alpha`

`= 0.cos alpha - 1.sin alpha`

`= -sin alpha`

`=>` $\cot (\dfrac{9\pi}{2}+ \alpha)=\dfrac{\cos (\dfrac{9\pi}{2}+\alpha)}{\sin (\dfrac{9\pi}{2}+\alpha)}$

`=(-sin alpha)/(cos alpha)=-tan alpha`