If cos(theta_1) + cos(theta_2) + cos(theta_3) | vedclass

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(D) Given,$\cos(	heta_1) + \cos(	heta_2) + \cos(	heta_3) + \cos(	heta_4) = -4$. Since the range of the cosine function is $[-1, 1]$,the only way t

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(D) Given,$\cos(	heta_1) + \cos(	heta_2) + \cos(	heta_3) + \cos(	heta_4) = -4$. Since the range of the cosine function is $[-1, 1]$,the only way their sum can be $-4$ is if each term is equal to $-1$. Thus,$\cos(	heta_1) = \cos(	heta_2) = \cos(	heta_3) = \cos(	heta_4) = -1$. This implies $	heta_1 = 	heta_2 = 	heta_3 = 	heta_4 = (2n+1)\pi$ for some integer $n$. Taking $	heta_i = \pi$,we have $\frac{	heta_i}{2} = \frac{\pi}{2}$. Then,$\cot(\frac{	heta_i}{2}) = \cot(\frac{\pi}{2}) = 0$. Therefore,$\cot(\frac{	heta_1}{2}) + \cot(\frac{	heta_2}{2}) + \cot(\frac{	heta_3}{2}) + \cot(\frac{	heta_4}{2}) = 0 + 0 + 0 + 0 = 0$.

If $\cos(\theta_1) + \cos(\theta_2) + \cos(\theta_3) + \cos(\theta_4) = -4$,then the value of $\cot(\frac{\theta_1}{2}) + \cot(\frac{\theta_2}{2}) + \cot(\frac{\theta_3}{2}) + \cot(\frac{\theta_4}{2}) = $

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