Question Number 46814 by peter frank last updated on 31/Oct/18
Answered by tanmay.chaudhury50@gmail.com last updated on 01/Nov/18
$${cos}\theta=\frac{{OP}^{\mathrm{2}} +{OQ}^{\mathrm{2}} −{PQ}^{\mathrm{2}} }{\mathrm{2}×{OP}×{OQ}} \\ $$$$\:\:\:=\frac{\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)+\left({c}^{\mathrm{2}} +{d}^{\mathrm{2}} \right)−\left\{\left({a}−{c}\right)^{\mathrm{2}} +\left({b}−{d}\right)^{\mathrm{2}} \right\}}{\mathrm{2}×\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\:×\sqrt{{c}^{\mathrm{2}} +{d}^{\mathrm{2}} }\:} \\ $$$$\:=\frac{{ac}+{bd}}{\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\:×\sqrt{{c}^{\mathrm{2}} +{d}^{\mathrm{2}} }\:} \\ $$
Commented by peter frank last updated on 01/Nov/18
$$\mathrm{thank}\:\mathrm{you} \\ $$