`c.`

Ta có:

`(sin\alpha+cos\alpha)²`

`=sin²\alpha+2sin\alpha.cos\alpha+cos²\alpha`

`=1+2.(12)/(25)`

`=(49)/(25)`

Mà `sin\alpha+cos\alpha>0`

`=>sin\alpha+cos\alpha=7/5`

`C=sin³\alpha+cos³\alpha`

`=(sin\alpha+cos\alpha)(sin²\alpha-sin\alpha.cos\alpha+cos²\alpha)`

`=7/5 . (1-(12)/(25))=(91)/(125)`

`d.`

`tan\alpha-cot\alpha=3`

`=>(tan\alpha-cot\alpha)²=9`

`<=>tan²\alpha-2tan\alpha.cot\alpha+cot²\alpha=9`

`<=>tan²\alpha-2+cot²\alpha=9`

`<=>tan²\alpha+cot²\alpha=11`

Cộng `2` vào hai vế

`=>tan²\alpha+2+cot²\alpha=13`

`=tan²\alpha+2tan\alpha.cot\alpha+cot²\alpha=13`

`<=>(tan\alpha+cot\alpha)²=13`

`<=>tan\alpha+cot\alpha=±\sqrt{13}`