Question

sin 16° sin 32° + cos 8º cos 56° = cos 24° cos40°​

Answer 1

$\large \bf{ \underline{To \: Prove :-}}$

• sin16° sin32° + cos8º cos56° = cos24° cos40°

$\large\bf{ \underline{Solution:-}}$

$• \sf{ \: L.H.S. }$

$\sf{= sin 16º sin 32º + cos 8º cos 56º}$

$\sf{= 0.28 \times 0.53 + 0.99 \times 0.56}$

$\sf{ =0.1484 + 0.5544 }$

$\sf{ =0.7028 } \: \: \: (approximately)$

$• \sf{ \: R.H.S}$

$= \sf{cos 24ºcos40º}$

$= \sf{0.91 \times 0.77}$

$= \sf {0.7007 \: \: \: (approximately)}$

$\sf{Hence, \:these \: values \: are \: quite \: same.}$

$\sf{\therefore{ L.H.S. = R.H.S}} \: \: \: \: \: \bold{[Proved]}$