1+cos⁡10∘+cos⁡20∘+cos⁡30∘=

4 sin ⁡ 10 ∘ sin ⁡ 20 ∘ sin ⁡ 30 ∘

1+cos⁡10∘+cos⁡20∘+cos⁡30∘=

4 sin ⁡ 10 ∘ sin ⁡ 20 ∘ sin ⁡ 30 ∘

4 cos ⁡ 10 ∘ cos ⁡ 20 ∘ cos ⁡ 30 ∘

4 cos ⁡ 5 ∘ cos ⁡ 10 ∘ cos ⁡ 15 0

4 sin ⁡ 5 ∘ sin ⁡ 10 ∘ sin ⁡ 15 ∘

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$1 + \cos 10^{\circ} + \cos 20^{\circ} + \cos 30^{\circ} =$

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$4 \sin 10^{\circ} \sin 20^{\circ} \sin 30^{\circ}$

$4 \cos 10^{\circ} \cos 20^{\circ} \cos 30^{\circ}$

$4 \cos 5^{\circ} \cos 10^{\circ} \cos 15^{0}$

$4 \sin 5^{\circ} \sin 10^{\circ} \sin 15^{\circ}$

answer is A.

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Detailed Solution

$\begin{array}{l} 1 + \cos 10^{\circ} + \cos 20^{\circ} + \cos 30^{\circ} \\ = 1 + 2 \cos^{2} 5 ° - 1 + 2 \cos 25 ° \cos 5 ° \\ = 2 \cos 5 ° (\cos 5 ° + \cos 25 °) \\ = 2 \cos 5 ° . (2 \cos 15^{\circ} \cos 10^{\circ}) = 4 \cos 5^{\circ} \cos 10^{\circ} \cos 15^{\circ} \end{array}$

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