Question

Show that:

$\sin {38}^{\circ }\cos {22}^{\circ }+\cos {38}^{\circ }\sin {22}^{\circ }=\frac{\sqrt{3}}{2}$

Answer 1

$\sin {38}^{\circ }\cos {22}^{\circ }+\sin {38}^{\circ }\sin {22}^{\circ }$

$\sin (A+B)=\sin A\cos B+\cos A\sin B$

$A={38}^{\circ },B={22}^{\circ }$

$A+B={60}^{\circ }$

$\therefore \sin {38}^{\circ }\cos {22}^{\circ }+\sin {38}^{\circ }\sin {22}^{\circ }=\sin {60}^{\circ }=\frac{\sqrt{3}}{2}$