The value of cos 24^{circ} + cos 55^{circ} + | vedclass

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Question

(A) We use the trigonometric identities: $\cos(180^{\circ} + 	heta) = -\cos 	heta$ and $\cos(360^{\circ} - 	heta) = \cos 	heta$.Given expression:

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$\frac{1}{2}$

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(A) We use the trigonometric identities: $\cos(180^{\circ} + 	heta) = -\cos 	heta$ and $\cos(360^{\circ} - 	heta) = \cos 	heta$.Given expression: $E = \cos 24^{\circ} + \cos 55^{\circ} + \cos 125^{\circ} + \cos 204^{\circ} + \cos 300^{\circ}$.$1$. $\cos 125^{\circ} = \cos(180^{\circ} - 55^{\circ}) = -\cos 55^{\circ}$.$2$. $\cos 204^{\circ} = \cos(180^{\circ} + 24^{\circ}) = -\cos 24^{\circ}$.$3$. $\cos 300^{\circ} = \cos(360^{\circ} - 60^{\circ}) = \cos 60^{\circ} = \frac{1}{2}$.Substituting these values into the expression:$E = \cos 24^{\circ} + \cos 55^{\circ} - \cos 55^{\circ} - \cos 24^{\circ} + \frac{1}{2}$.$E = 0 + 0 + \frac{1}{2} = \frac{1}{2}$.

The value of $\cos 24^{\circ} + \cos 55^{\circ} + \cos 125^{\circ} + \cos 204^{\circ} + \cos 300^{\circ}$ is

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