Prove that: 1^ 2^ 3^ 180^ =0 - Vidyadip

Question

Prove that:
$\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos180^\circ=0$

✓

Answer

$\text{L.H.S.}=\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos180^\circ$
$=\cos1^\circ\times\cos2^\circ\times\cos3^\circ\times\dots\cos90^\circ\times\dots\cos180^\circ$
$=\cos1^\circ\times\cos2^\circ\times\cos3^\circ\times\dots\times0\times\dots\cos180^\circ$
$=0$
$=\text{R.H.S.}$

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