First slide

Properties of ITF

Question

If $A = \tan^{- 1} (\frac{x \sqrt{3}}{2 k - x})$ and $B = \tan^{- 1} (\frac{2 x - k}{k \sqrt{3}})$ then the value of A – B is

Moderate

A

0⁰
B

45⁰
C

60⁰
D

30⁰

Solution

$\begin{array}{l} \tan (A - B) = \frac{\tan A + \tan B}{1 + \tan Atan B} \\ = \frac{\frac{x \sqrt{3}}{2 k - x} - \frac{2 x - k}{k \sqrt{3}}}{1 + \frac{x \sqrt{3}}{2 k - x} \cdot \frac{2 x - k}{k \sqrt{3}}} = \frac{1}{\sqrt{3}} \\ ∴ A - B = 30^{\circ} \end{array}$

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