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2. inverse trigonometric function — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths2. inverse trigonometric function1 Mark
MCQ
$2{\tan ^{ - 1}}\left( {\frac{1}{3}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right) = $
  • A
    ${\tan ^{ - 1}}\left( {\frac{{49}}{{29}}} \right)$
  • B
    $\frac{\pi }{2}$
  • C
    $0$
  • ✓
    $\frac{\pi }{4}$
✓

Answer

Correct option: D.
$\frac{\pi }{4}$
d
(d) $2{\tan ^{ - 1}}\left( {\frac{1}{3}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right) = {\tan ^{ - 1}}\left( {\frac{{2(1/3)}}{{1 - (1/9)}}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right)$

$ = {\tan ^{ - 1}}\frac{3}{4} + {\tan ^{ - 1}}\frac{1}{7} = {\tan ^{ - 1}}\left( {\frac{{(3/4) + (1/7)}}{{1 - (3/4) \times (1/7)}}} \right)$

$ = {\tan ^{ - 1}}\left( {\frac{{25}}{{25}}} \right) = \frac{\pi }{4}$.

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