Question

Show that:
$cos{38}^{\circ }cos{52}^{\circ }-sin{38}^{\circ }sin{52}^{\circ }=0$

Answer 1

$\cos {38}^o\cos {52}^o-\sin {30}^o\sin {52}^o$

$\Rightarrow \cos (90-{52}^o)\cos ({90}^o-{38}^o)-\sin {30}^o\sin {52}^o$

$\Rightarrow \sin {52}^o\sin {38}^o-\sin {38}^o\sin {52}^o$

$\Rightarrow 0$.