দেওয়া আছে, $x=r \sin(\theta+45^{\circ})$ এবং $y=r \sin(\theta-45^{\circ})$। $$ \begin{aligned} x^2+y^2 &= r^2 \sin^2(\theta+45^{\circ}) + r^2 \sin^2(\theta-45^{\circ}) \\ &= r^2 \left[ \sin^2(\theta+45^{\circ}) + \sin^2(\theta-45^{\circ}) \right] \\ &= r^2 \left[ \frac{1-\cos(2\theta+90^{\circ})}{2} + \frac{1-\cos(2\theta-90^{\circ})}{2} \right] \\ &= \frac{r^2}{2} \left[ 2 - (\cos(2\theta+90^{\circ}) + \cos(2\theta-90^{\circ})) \right] \\ &= \frac{r^2}{2} \left[ 2 - (-\sin 2\theta + \sin 2\theta) \right] \\ &= \frac{r^2}{2} \times 2 \\ &= r^2 \end{aligned} $$