If
1−sinA
cosAcotA
​
=x, then the value of x is

Given expression:
x=
1−sinA
cosAcotA
​

Substitute cotA=
sinA
cosA
​
:

x=
1−sinA
cosA⋅
sinA
cosA
​

​
=
sinA(1−sinA)
cos
2
A
​

Using the identity cos
2
A=1−sin
2
A:

x=
sinA(1−sinA)
1−sin
2
A
​

Factorise the numerator as a difference of squares (a
2
−b
2
=(a−b)(a+b)):

x=
sinA(1−sinA)
(1−sinA)(1+sinA)
​

Cancel out the common term (1−sinA) from the numerator and denominator:

x=
sinA
1+sinA
​

Split the fraction:

x=
sinA
1
​
+
sinA
sinA
​

x=cscA+1⟹1+cscA