\(VT=\dfrac{sin^3\left(\dfrac{pi}{2}-\dfrac{A+C}{2}\right)}{cos\left(\dfrac{A+C}{2}\right)}+\dfrac{cos^3\left(\dfrac{pi}{2}-\dfrac{A+C}{2}\right)}{sin\left(\dfrac{A+C}{2}\right)}-\dfrac{cos\left(180^0-B\right)}{sinB}\cdot tanB\)
\(=cos^2\left(\dfrac{A+C}{2}\right)+sin^2\left(\dfrac{A+C}{2}\right)+\dfrac{cos\left(B\right)}{sinB}\cdot tanB\)
=1+1
=2=VP