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JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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If A>0,B>0\mathrm{A}>0, \mathrm{B}>0 and A+B=π6\mathrm{A}+\mathrm{B}=\frac{\pi}{6}, then the minimum value of tan⁡A+tan⁡B\tan \mathrm{A}+\tan \mathrm{B} is :
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Correct option: B
4−234-2 \sqrt{3}
Option B (4−234-2 \sqrt{3}) is correct because by using the tangent addition formula and AM-GM inequality, we find the minimum value of tan⁡A+tan⁡B\tan A + \tan B to be 4−234-2\sqrt{3}.

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