The value of cos 24^{circ} + cos 5^{circ} + c | vedclass

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Question

(C) Given expression: $\cos 24^{\circ} + \cos 5^{\circ} + \cos 300^{\circ} + \cos 175^{\circ} + \cos 204^{\circ}$Using trigonometric identities:$\cos

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$\frac{1}{2}$

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(C) Given expression: $\cos 24^{\circ} + \cos 5^{\circ} + \cos 300^{\circ} + \cos 175^{\circ} + \cos 204^{\circ}$Using trigonometric identities:$\cos 300^{\circ} = \cos(360^{\circ} - 60^{\circ}) = \cos 60^{\circ} = \frac{1}{2}$$\cos 175^{\circ} = \cos(180^{\circ} - 5^{\circ}) = -\cos 5^{\circ}$$\cos 204^{\circ} = \cos(180^{\circ} + 24^{\circ}) = -\cos 24^{\circ}$Substituting these values into the expression:$= \cos 24^{\circ} + \cos 5^{\circ} + \frac{1}{2} - \cos 5^{\circ} - \cos 24^{\circ}$Canceling the terms:$= \frac{1}{2}$

The value of $\cos 24^{\circ} + \cos 5^{\circ} + \cos 300^{\circ} + \cos 175^{\circ} + \cos 204^{\circ}$ is

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