Show that: $$\cos[i\log(2+\sqrt3)]=2$$
I attempted by taking$(2+\sqrt3)$ into trigonometrical form but i am stuck Please help me out.
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Funfact: $2+\sqrt3=\tan(\frac5{12}\pi)$. However I don't think this helps you, see Olivier's answer instead :) – David Jun 27 '16 at 07:19
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What's the trigonometrical form of $2+\sqrt3$ ? – Jun 27 '16 at 12:10
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$\cos\left(x,\mathrm{i}\right) = ,\mathrm{cosh}\left(x\right)$. – Felix Marin Jun 27 '16 at 17:30
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Hint. One may recall that $$ \cos z= \frac{e^{iz}+e^{-iz}}2, \quad z \in \mathbb{C}. $$ Apply it with $z=i \log(2+\sqrt{3})$.
Olivier Oloa
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