Đáp án:
Ta có:`sin^2\alpha+cos^2\alpha=1`
`<=>4/25+cos^2\alpha=1`
`<=>cos^2\alpha=1-4/25=21/25`
`<=>cos\alpha=\sqrt{21}/5`
`cot\alpha=(cos\alpha)/(sin\alpha)`
$=\dfrac{\dfrac{\sqrt{21}}{5}}{\dfrac{2}{5}}$
`=\sqrt{21}/2`
`5cos^2\alpha-2sin^2\alpha+3cot\alpha`
`=7cos^2\alpha-2cos^2\alpha-2sin^2+(3\sqrt{21})/2`
`=7*21/5-2(sin^2\alpha+cos^2\alpha)+(3\sqrt{21})/2`
`=147/5-2+(3\sqrt{21})/2`
`=137/5+(3\sqrt{21})/2`
`=(274+15\sqrt{21})/10`
