If f(theta) = cos theta_1 cdot cos theta_2 cd | vedclass

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Question

(A) Given the function $f(	heta) = \cos 	heta_1 \cdot \cos 	heta_2 \cdot \cos 	heta_3 \cdots \cos 	heta_n$. Taking the natural logarithm on both

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$\frac{-f^{\prime}(	heta)}{f(	heta)}$

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(A) Given the function $f(	heta) = \cos 	heta_1 \cdot \cos 	heta_2 \cdot \cos 	heta_3 \cdots \cos 	heta_n$. Taking the natural logarithm on both sides,we get: $\ln(f(	heta)) = \ln(\cos 	heta_1) + \ln(\cos 	heta_2) + \cdots + \ln(\cos 	heta_n)$. Differentiating both sides with respect to $	heta$ (assuming $	heta$ represents the set of variables $	heta_1, 	heta_2, \dots, 	heta_n$): $\frac{1}{f(	heta)} \cdot f^{\prime}(	heta) = \frac{1}{\cos 	heta_1} \cdot (-\sin 	heta_1) \cdot \frac{d	heta_1}{d	heta} + \cdots + \frac{1}{\cos 	heta_n} \cdot (-\sin 	heta_n) \cdot \frac{d	heta_n}{d	heta}$. If we consider the derivative with respect to the individual variables or the sum of logarithmic derivatives,we observe that $\frac{f^{\prime}(	heta)}{f(	heta)} = -(	an 	heta_1 + 	an 	heta_2 + \cdots + 	an 	heta_n)$. Therefore,$	an 	heta_1 + 	an 	heta_2 + \cdots + 	an 	heta_n = -\frac{f^{\prime}(	heta)}{f(	heta)}$.

If $f(\theta) = \cos \theta_1 \cdot \cos \theta_2 \cdot \cos \theta_3 \cdots \cos \theta_n$,then $\tan \theta_1 + \tan \theta_2 + \tan \theta_3 + \cdots + \tan \theta_n =$

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