The value of 1+cos⁡56∘+cos⁡58∘−cos⁡66∘is equal to

4 cos ⁡ 28 ∘ cos ⁡ 29 ∘ sin ⁡ 33 ∘

The value of 1+cos⁡56∘+cos⁡58∘−cos⁡66∘is equal to

4 cos ⁡ 28 ∘ cos ⁡ 29 ∘ sin ⁡ 33 ∘

2 cos ⁡ 28 ∘ cos ⁡ 29 ∘ sin ⁡ 33 ∘

4 cos ⁡ 28 ∘ cos ⁡ 29 ∘ cos ⁡ 33 ∘

4 cos ⁡ 28 ∘ cos ⁡ 29 ∘ sin ⁡ 33 ∘

2 cos ⁡ 28 ∘ cos ⁡ 29 ∘ cos ⁡ 33 ∘

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The value of $1 + \cos 56^{\circ} + \cos 58^{\circ} - \cos 66^{\circ}$ is equal to

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$2 \cos 28^{\circ} \cos 29^{\circ} \sin 33^{\circ}$

$4 \cos 28^{\circ} \cos 29^{\circ} \cos 33^{\circ}$

$4 \cos 28^{\circ} \cos 29^{\circ} \sin 33^{\circ}$

$2 \cos 28^{\circ} \cos 29^{\circ} \cos 33^{\circ}$

answer is C.

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Detailed Solution

$\begin{aligned} 1 + \cos 56^{\circ} + \cos 58^{\circ} - \cos 66^{\circ} \\ = 2 \cos^{2} 28^{\circ} + 2 \sin 62^{\circ} \sin 4^{\circ} \\ = 2 \cos^{2} 28^{\circ} + 2 \cos 28^{\circ} \cos 86^{\circ} \\ = 2 \cos 28^{\circ} (\cos 28^{\circ} + \cos 86^{\circ}) \\ = 2 \cos 28^{\circ} (2 \cos 57^{\circ} \cos 29^{\circ}) \\ = 4 \cos 28^{\circ} \cos 29^{\circ} \cos 33^{\circ} \end{aligned}$