If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-2px+\left ( p^{2} + q^{2}\right )=0$ and $tan \; \theta =\large \frac{q}{y+p}$ show that $\large\frac{\left (y+\alpha \right )^{n}-\left ( y+\beta \right )^{n}}{\alpha -\beta }$ = $q^{n-1}\large\frac{sin \;n\theta }{sin\;^{n}\theta }$

Question

n ∈ N