Question

if tanA=√3,tanB=2-√3 show thatA-B=pi/4​

Answer 1

Answer:

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Answer 2

$\displaystyle \tan(A-B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}\\\\\\ \tan(A-B) = \frac{ \sqrt{3 } - (2 - \sqrt{3})}{1 + \sqrt{3} ({2-\sqrt{3}})}\\\\\\ = \frac{-2 + 2 \sqrt{3}}{-2 + 2 \sqrt3}} = 1}\\\\\\\tan(A - B) = 1\\\\\therefore A - B = \frac{\pi}{4}$