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

We know the half-angle formula for cotangent:
cot(
2
A
​
)=
sin(
2
A
​
)
cos(
2
A
​
)
​

Multiply both the numerator and the denominator by 2sin(
2
A
​
):

x=
2sin
2
(
2
A
​
)
2cos(
2
A
​
)sin(
2
A
​
)
​

Using the double-angle identities:

2sin(
2
A
​
)cos(
2
A
​
)=sinA
2sin
2
(
2
A
​
)=1−cosA
Substituting these back into the expression gives:

x=
1−cosA
sinA
​