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dhruvi62

25.04.2020

Mathematics

$2-\sqrt{3}$

Step-by-step explanation:

$tan15 = tan(45 - 30)=\frac{\tan{45}-\tan{30}}{1+\tan{45}\tan{30}}\\\\=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}\\\\\\=\frac{\sqrt{3}-1}{\sqrt{3}+1}\\\\\\$

$=\frac{(\sqrt{3}-1)^2}{3-1}\\=\frac{3+1-2\sqrt{3}}{2}\\=2-\sqrt{3}$

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