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I want to simply the following without use of a calculator: $\displaystyle \frac{2 \tan⁡64°}{1-\tan^2⁡64°}$

At first I thought that this is tangent double angle identity = $\tan(2\times 64°) $

hence $=\tan(128°) $

Is that all? Really?

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$\displaystyle Yup,\ that's\ it.$

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  • $\begingroup$ Double play here! $\endgroup$ – ncmathsadist Nov 2 '13 at 0:36
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Yes, you are correct, $$ \frac{2 \tan⁡x}{1-\tan^2x} = \tan 2x. $$ The given problem is absolutely in the given format. Therefore, you directly use this principle to get the required solution that you have already got.

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