\(A=1+\sin\left(\dfrac{x}{2}\right)\cdot\sin x-\cos\left(\dfrac{x}{2}\right)\cdot\sin^2x-2\cdot\dfrac{1+\cos\left(\dfrac{\Pi}{2}-x\right)}{2}\)
\(=1+\sin\left(\dfrac{x}{2}\right)\cdot\sin x-\cos\left(\dfrac{x}{2}\right)\cdot\sin^2x-1-\sin x\)
\(=\sin x\left[\sin\left(\dfrac{x}{2}\right)-\cos\left(\dfrac{x}{2}\right)\cdot\sin x-1\right]\)