If
1+cosA
1−cosA
​
=x, then the value of x is:

Given expression:
x=
1+cosA
1−cosA
​

Rationalizing the numerator or the denominator, let's multiply both the numerator and the denominator by (1−cosA):

x=
(1+cosA)(1−cosA)
(1−cosA)(1−cosA)
​

x=
1−cos
2
A
(1−cosA)
2

​

Since 1−cos
2
A=sin
2
A:

x=
sin
2
A
(1−cosA)
2

​

x=(
sinA
1−cosA
​
)
2

x=(
sinA
1
​
−
sinA
cosA
​
)
2

x=(cscA−cotA)
2

Since (a−b)
2
=(b−a)
2
, this can also be written as:

x=(cotA−cscA)
2