$c o s 55^{\circ} + c o s 65^{\circ} + c o s 175^{\circ} =$ ___

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- 1

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\sqrt{2}

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Solution

$2 c o s (\frac{55^{\circ} + 65^{\circ}}{2}) c o s (\frac{55^{\circ} - 65^{\circ}}{2}) + c o s 175^{\circ}$
$\Rightarrow 2 c o s 60^{\circ} c o s 5^{\circ} - c o s 5^{\circ}$
$\Rightarrow 2 \times \frac{1}{2} c o s 5^{\circ} - c o s 5^{\circ} = 0$

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