If A>0,B>0 and A+B=π6then the minimum value of tan⁡A+tan⁡B is

# If then the minimum value of $\mathrm{tan}A+\mathrm{tan}B$ is

1. A

$\sqrt{3}-\sqrt{2}$

2. B

$4-2\sqrt{3}$

3. C

$\frac{2}{\sqrt{3}}$

4. D

$2-\sqrt{3}$

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### Solution:

We know that, $\mathrm{tan}\left(A+B\right)=\frac{\mathrm{tan}A+\mathrm{tan}B}{1-\mathrm{tan}A\mathrm{tan}B}$

Also

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