cos 1^circ + cos 2^circ + cos 3^circ + dots + | vedclass

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(C) The given expression is $S = \sum_{k=1}^{180} \cos k^\circ$.We know that $\cos(180^\circ - 	heta) = -\cos 	heta$.Thus,$\cos 179^\circ = -\cos 1^

Vedclass · Accepted Answer

$-1$

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(C) The given expression is $S = \sum_{k=1}^{180} \cos k^\circ$.We know that $\cos(180^\circ - 	heta) = -\cos 	heta$.Thus,$\cos 179^\circ = -\cos 1^\circ$,$\cos 178^\circ = -\cos 2^\circ$,and so on.Pairing the terms: $(\cos 1^\circ + \cos 179^\circ) + (\cos 2^\circ + \cos 178^\circ) + \dots + (\cos 89^\circ + \cos 91^\circ) + \cos 90^\circ + \cos 180^\circ$.Each pair sums to $0$ because $\cos 	heta + \cos(180^\circ - 	heta) = 0$.Since $\cos 90^\circ = 0$ and $\cos 180^\circ = -1$,the total sum is $0 + 0 + \dots + 0 + 0 + (-1) = -1$.

$\cos 1^\circ + \cos 2^\circ + \cos 3^\circ + \dots + \cos 180^\circ = $

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