The value of cos 52^circ + cos 68^circ + cos | vedclass

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(A) Using the sum-to-product formula $\cos C + \cos D = 2 \cos \left( \frac{C+D}{2} \right) \cos \left( \frac{C-D}{2} \right)$:$\cos 52^\circ + \cos 1

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(A) Using the sum-to-product formula $\cos C + \cos D = 2 \cos \left( \frac{C+D}{2} \right) \cos \left( \frac{C-D}{2} \right)$:$\cos 52^\circ + \cos 172^\circ + \cos 68^\circ$$= 2 \cos \left( \frac{52^\circ + 172^\circ}{2} \right) \cos \left( \frac{52^\circ - 172^\circ}{2} \right) + \cos 68^\circ$$= 2 \cos (112^\circ) \cos (-60^\circ) + \cos 68^\circ$Since $\cos (-60^\circ) = \cos 60^\circ = \frac{1}{2}$:$= 2 \cos (112^\circ) \left( \frac{1}{2} \right) + \cos 68^\circ$$= \cos 112^\circ + \cos 68^\circ$$= \cos (180^\circ - 68^\circ) + \cos 68^\circ$$= -\cos 68^\circ + \cos 68^\circ = 0$.

The value of $\cos 52^\circ + \cos 68^\circ + \cos 172^\circ$ is

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