cos^3 110^{circ} + cos^3 10^{circ} + cos^3 13 | vedclass

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Question

(C) We use the trigonometric identity: $\cos^3 x + \cos^3(120^{\circ} - x) + \cos^3(120^{\circ} + x) = \frac{3}{4} \cos(3x)$.Given the expression $\co

Vedclass · Accepted Answer

$\frac{3\sqrt{3}}{8}$

Vedclass · Answer

(C) We use the trigonometric identity: $\cos^3 x + \cos^3(120^{\circ} - x) + \cos^3(120^{\circ} + x) = \frac{3}{4} \cos(3x)$.Given the expression $\cos^3 10^{\circ} + \cos^3 110^{\circ} + \cos^3 130^{\circ}$,we can rewrite it as:$\cos^3 10^{\circ} + \cos^3(120^{\circ} - 10^{\circ}) + \cos^3(120^{\circ} + 10^{\circ})$.Here,$x = 10^{\circ}$.Applying the identity:$= \frac{3}{4} \cos(3 	imes 10^{\circ})$$= \frac{3}{4} \cos 30^{\circ}$$= \frac{3}{4} 	imes \frac{\sqrt{3}}{2}$$= \frac{3\sqrt{3}}{8}$.

$\cos^3 110^{\circ} + \cos^3 10^{\circ} + \cos^3 130^{\circ} = $

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