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

Question

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

Dr. Abubacker · Accepted Answer

(d)
We know that,
$	an{(A - B) = \frac{	an{A - 	an B}}{1 + 	an{A	an B}}}$
$= \frac{\frac{x\sqrt{3}}{2k - x} - \frac{2x - k}{k\sqrt{3}}}{1 + \frac{x\sqrt{3}}{2k - x}.\frac{2x - k}{k\sqrt{3}}} = \frac{1}{\sqrt{3}}$
$\Rightarrow A - B = 30{^\circ}$

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

Explanation

Reviewed by Dr. Abubacker

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