If cot(
2
A
​
)=x, then the value of x is:

We know the standard half-angle trigonometric formulas:
cosA=2cos
2
(
2
A
​
)−1⟹1+cosA=2cos
2
(
2
A
​
)
cosA=1−2sin
2
(
2
A
​
)⟹1−cosA=2sin
2
(
2
A
​
)
Dividing the first equation by the second:

1−cosA
1+cosA
​
=
2sin
2
(
2
A
​
)
2cos
2
(
2
A
​
)
​
=cot
2
(
2
A
​
)
Taking the square root on both sides:

cot(
2
A
​
)=
1−cosA
1+cosA
​


​

Since x=cot(
2
A
​
), we get:

x=
1−cosA
1+cosA
​


​