# How do you verify sin^2 ( x/2) = (cscx-cotx)/(2cscx)?

RHS $= \frac{\csc x - \cot x}{2 \csc x}$
$= \frac{\sin x \left(\csc x - \cot x\right)}{2 \sin x \cdot \csc x}$ Multiplying both numerator and denominator by sinx
$= \frac{\sin x \cdot \csc x - \sin x \cdot \cot x}{2}$
$= \frac{1 - \cos x}{2} = \frac{2 {\sin}^{2} \left(\frac{x}{2}\right)}{2}$
$= {\sin}^{2} \left(\frac{x}{2}\right) = L H S$