Question

Evaluate the following:$\sin {78}^o\cos {18}^o-\cos {78}^o\sin {18}^o$

Answer 1

Applying the trigonometric identity in $\sin {78}^{\circ }\cos {18}^{\circ }-\cos {78}^{\circ }\sin {18}^{\circ }$.

$\sin {78}^{\circ }\cos {18}^{\circ }-\cos {78}^{\circ }\sin {18}^{\circ }=\sin \left({78}^{\circ }-{18}^{\circ }\right)$

$=\sin {60}^{\circ }$

$=\frac{\sqrt{3}}{2}$