Ta có:

`1+ cot^2 \alpha = 1/(sin^2 \alpha)`

`sin^2 \alpha . (1 + cot^2 \alpha) =1`

`sin^2 \alpha  = 1/(1 + cot^2 \alpha)`

Ta có:

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

`=> cos \alpha = cot \alpha . sin \alpha`

Ta có:
`2. cos^2 \alpha + 5 . sin \alpha . cos \alpha +1`

`= 2. ( cot \alpha . sin \alpha)^2 + 5. sin \alpha . cot \alpha . sin \alpha +1`

`= 2. cot^2 \alpha . 1/(1+ cot^2 \alpha) + 5. 1/(1+cot^2 \alpha) . cot\alpha +1`

`= 2. 5^2 . 1/(1 + 5^2) +5/(1 + 5^2) . 5 +1`

`= 50 . 1/(26) + 25/(26) +1`

`= 25/13 + 25/26 +1`

`=101/26`.