In ABC (with usual notations); a = 2b and |A - B| = then which of the following doesn't hold good?

JEE MainMathematicsModerate

In $\Delta$ ABC (with usual notations); a = 2b and |A - B| =
$\frac{\pi}{3}$ then which of the following doesn't hold good?

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A - B = \frac{\pi}{3}

\tan\left( \frac{A - B}{2} \right) = \frac{a - b}{a + b}cos\frac{C}{2}

tan30^{\circ} = \frac{1}{3}cot\frac{C}{2}

C = 60°;
A - B = 60°; A + B = 120°

\therefore\

A = 90° and B = 30°

Source: Grass-G / M-24 Mathematics Paper 31 Dec.docx

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