If A,B,C are angles of a triangle, then `2sin(A/2)cosec (B/2)sin(C/2)-sinAcot(B/2)-cosA` is (a)independent of A,B,C (b) function of A,B (c)function of C (d) none of these

Explanation

To solve the problem, we need to simplify the expression given:

\[ K = 2\sin\left(\frac{A}{2}\right) \csc\left(\frac{B}{2}\right) \sin\left(\frac{C}{2}\right) - \sin A \cot\left(\frac{B}{2}\right) - \cos A \]

### Step 1: Rewrite the expression using trigonometric identities

We know that \( \csc\left(\frac{B}{2}\right) = \frac{1}{\sin\left(\frac{B}{2}\right)} \). Therefore, we can rewrite the first term:

...