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  4. sin 10° + sin 20° + sin 30° + ldots ldots + sin 360° is equal to

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Q. $\sin 10^\circ +\sin 20^\circ +\sin 30^\circ +\ldots \ldots +\sin 360^\circ $ is equal to

NTA AbhyasNTA Abhyas 2022

Solution:

Given:
$\sin 10^{\circ}+\sin 20^{\circ}+\sin 30^{\circ}+\ldots+\sin 270^{\circ}+\sin 360^{\circ}$
$\because \sin 190^{\circ}=\sin \left(180^{\circ}+10^{\circ}\right)=-\sin 10^{\circ}$
$\sin 200^{\circ}=-\sin 20^{\circ} $
$\sin 210^{\circ}=-\sin 30^{\circ} $
$\sin 360^{\circ}=\sin 180^{\circ}=0$
$\therefore $ Given expression is equal to zero.