Question

Show that $cos{1}^{0}cos{2}^{{}^0}cos{3}^0.........cos{180}^0=0$

Answer 1

To prove:- $\cos 1°\cdot \cos 2°\cdot \cos 3°\cdot .....\cdot \cos 90°\cdot .....\cdot \cos 180°=0$

Proof:-

Taking L.H.S.-

$\cos 1°\cdot \cos 2°\cdot \cos 3°\cdot .....\cdot \cos 90°\cdot .....\cdot \cos 180°$

$\because \cos 90°=0$

$\therefore \cos 1°\cdot \cos 2°\cdot \cos 3°\cdot .....\cdot \cos 90°\cdot .....\cdot \cos 180°=0=$R.H.S.

Hence proved.