Theo gt:

`cot alpha + cot gamma = 2 cot beta`

`cot beta={cot alpha + cot gamma}/2` `(1)`

`alpha + beta + gamma = {pi}/2`

`alpha + gamma = {pi}/2 - beta`

`tan (alpha + gamma)= tan ({pi}/2 - beta)=cot beta` `(2)`

Mặt khác:

`tan (alpha + gamma)`

`={tan alpha + tan gamma}/{1-tan alpha tan gamma}`

`={1/{cot alpha}+1/{cot gamma}}/{1-1/{cot alpha*cot gamma}}`

`={cot alpha + cot gamma}/{cot alpha*cot gamma -1}` `(3)`

Từ `(2)` và `(3)`:

`cot beta = {cot alpha + cot gamma}/{cot alpha*cot gamma -1}`

Thay vào `(1)`:

`{cot alpha + cot gamma}/2 = {cot alpha + cot gamma}/{cot alpha*cot gamma -1}`

`1/2=1/{cot alpha*cot gamma -1}`

`cot alpha*cot gamma -1=2`

`cot alpha*cot gamma=3`

`->` Chọn `C`