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If $A=\frac{\pi}{24}$, then $\frac{\cos A+\cos 3 A+\cos 5 A+\cos 7 A}{\sin A+\sin 3 A+\sin 5 A+\sin 7 A}=$
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$\sqrt{3}$
$\begin{aligned} & \text {Let } I=\frac{\cos A+\cos 3 A+\cos 5 A+\cos 7 A}{\sin A+\sin 3 A+\sin 5 A+\sin 7 A} \\ & \Rightarrow I=\frac{(\cos A+\cos 7 A)+(\cos 5 A+\cos 3 A)}{(\sin A+\sin 7 A)+(\sin 5 A+\sin 3 A)} \\ & \Rightarrow I=\frac{\cos 4 A[2 \cos 3 A+2 \cos A]}{\sin 4 A[2 \cos 3 A+2 \cos A]} \\ & \Rightarrow I=\cot 4 A=\cot \frac{\pi}{6}=\sqrt{3}\end{aligned}$
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