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Find $$\lim_{x\rightarrow \frac{\pi}{4}}\left(\frac{\sin x}{\cos x}\right)^\left(\frac{\sin 2x}{\cos 2x}\right)$$

My work so far: $$\lim_{x\rightarrow \frac{\pi}{4}}\left(\frac{\sin x}{\cos x}\right)^\left(\frac{\sin 2x}{\cos 2x}\right)=\lim_{x\rightarrow \frac{\pi}{4}}\tan^{\tan 2x}x=1^{\infty}$$

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  • $\begingroup$ probably take a log and use lopital $\endgroup$ – Tim kinsella Oct 31 '17 at 16:34
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HINT: write your term in the form $$e^{\lim_{x\to \frac{\pi}{4}}\frac{\ln(\tan(x)}{\cot(2x)}}$$ and use L'Hospital

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