Question

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

Answer 1

$\cos {38}^o\cos {52}^o-\sin {38}^o\sin {52}^o=0$
$LHS=cos{38}^{0}cos{52}^0-sin{38}^{0}sin{52}^0$
$=cos{38}^0\times cos(90-38)-sin{38}^0\times sin(90-38)$
$=cos{38}^0\times sin{38}^0-sin{38}^0\times cos{38}^0$
$=0$