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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
If $\tan ^{-1} \frac{a+x}{a}+\tan ^{-1} \frac{a-x}{a}=\frac{\pi}{6}$, then $x^2=$
  • A
    $2 \sqrt{3 a}$
  • B
    $\sqrt{3 a}$
  • ✓
    $2 \sqrt{3} a ^2$
  • D
    $\sqrt{3} a ^2$
✓

Answer

Correct option: C.
$2 \sqrt{3} a ^2$
(C) $\tan ^{-1} \frac{a+x}{a}+\tan ^{-1} \frac{a-x}{a}=\frac{\pi}{6}$
$\therefore \quad \tan ^{-1}\left(\frac{\frac{a+x}{a}+\frac{a-x}{a}}{1-\frac{a+x}{a} \cdot \frac{a-x}{a}}\right)=\frac{\pi}{6}$
$\therefore \quad \frac{2 a ^2}{x^2}=\tan \frac{\pi}{6}=\frac{1}{\sqrt{3}} \Rightarrow x^2=2 \sqrt{3} a ^2$

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