The value of \( \lim _{x \rightarrow 4} \frac{(\cos \alpha)^{x}-(\sin \alpha)^{x}-\cos 2 \alpha}...

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The value of \( \lim _{x \rightarrow 4} \frac{(\cos \alpha)^{x}-(\sin \alpha)^{x}-\cos 2 \alpha}{x-4}, \alpha \in\left(0, \frac{\pi}{2}\right) \) is
(a) \( \log (\cos \alpha)+(\sin \alpha)^{4} \log (\sin \alpha) \)
(b) \( \left(\cos ^{4} \alpha\right) \log (\cos \alpha)-(\sin \alpha)^{4} \log (\sin \alpha) \)
(c) \( \left(\cos ^{4} \alpha\right) \log (\cos \alpha) \)
(d) None of these
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