Question

Find the distance between P($a\sin \alpha ,-b\cos \alpha$) & Q($-a\cos \alpha ,b\sin \alpha$)

Answer 1

PQ = $\sqrt{(asin\alpha +acos\alpha {)}^2+(bsin\alpha +bcos\alpha {)}^2}$
PQ = $\sqrt{asi{n}^2\alpha +a^{2}co{s}^2\alpha +b^{2}si{n}^2\alpha +bco{s}^2\alpha }$
PQ = $\sqrt{a^2(si{n}^2\alpha +co{s}^2\alpha )+b^2(si{n}^2\alpha +co{s}^2\alpha )}$
PQ = $\sqrt{(si{n}^2\alpha +co{s}^2\alpha )a^2+b^2}$
PQ = $\sqrt{a^2+b^2\left(1\right)}$
PQ = $\sqrt{a^2+b^2}$