What is the simplest form of (1+cosA)(cscA−cotA)?

Let us simplify the given expression:
E=(1+cosA)(cscA−cotA)
We know that cscA=
sinA
1
​
and cotA=
sinA
cosA
​
. Substituting these values:

E=(1+cosA)(
sinA
1
​
−
sinA
cosA
​
)
E=(1+cosA)(
sinA
1−cosA
​
)
E=
sinA
(1+cosA)(1−cosA)
​

Using the identity (a+b)(a−b)=a
2
−b
2
:

E=
sinA
1−cos
2
A
​

Since sin
2
A+cos
2
A=1, we have 1−cos
2
A=sin
2
A:

E=
sinA
sin
2
A
​
=sinA