$cos 24^{0} + cos 5^{0} + cos 175^{0} + cos 204^{0} + cos 300^{0} =$

\frac{1}{2}

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\frac{- 1}{2}

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\frac{\sqrt{3}}{2}

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1

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Solution

The correct option is A $\frac{1}{2}$
We know that,
$cos 175^{\circ} = cos (180 - 5)^{\circ} = - cos 5^{\circ} cos 204^{\circ} = cos (180 + 24)^{\circ} = - cos 24^{\circ} cos 300^{\circ} = cos (270 + 30)^{\circ} = sin 30^{\circ}$

$\Rightarrow$ $cos 24^{\circ} + cos 5^{\circ} + cos 175^{\circ} + cos 204^{\circ} + cos 300^{\circ}$

$= cos 24^{\circ} + cos 5^{\circ} - cos 24^{\circ} - cos 5^{\circ} + sin 30^{\circ}$

$= sin 30^{\circ} = 1 / 2$

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