Find value of sin² 15º + sin² 645º :

${\sin }^2{15}^{\circ }+{\sin }^2\left({645}^{\circ }\right)$

$\begin{array}{l}\text{ Now, }\sin \left({645}^{\circ }\right)=\sin \left(7\times 90+{15}^{\circ }\right)\\ =-\cos {15}^{\circ }\\ \text{ So, }{\sin }^2{15}^{\circ }+{\left(-\cos {15}^{\circ }\right)}^2={\sin }^2{15}^{\circ }+{\cos }^2{15}^{\circ }=1.\end{array}$