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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths2. inverse trigonometric function1 Mark
MCQ
$\tan \left( {2{{\cos }^{ - 1}}\frac{3}{5}} \right) = $
  • A
    $\frac{7}{{25}}$
  • B
    $\frac{{24}}{{25}}$
  • ✓
    $ - \frac{{24}}{7}$
  • D
    $\frac{8}{3}$
✓

Answer

Correct option: C.
$ - \frac{{24}}{7}$
c
(c) $\tan \left( {2{{\cos }^{ - 1}}\frac{3}{5}} \right) = \tan \left[ {{{\cos }^{ - 1}}\left( {2.\frac{9}{{25}} - 1} \right)} \right]$

{Since $2{\cos ^{ - 1}}x = {\cos ^{ - 1}}(2{x^2} - 1)$}

$ = \tan {\cos ^{ - 1}}\left( { - \frac{7}{{25}}} \right) = \tan {\tan ^{ - 1}}\left[ {\sqrt {\frac{{1 - \frac{{49}}{{625}}}}{{ - \frac{7}{{25}}}}} } \right] = - \frac{{24}}{7}$

Therefore $\tan \left( {2{{\cos }^{ - 1}}\frac{3}{5}} \right) = - \frac{{24}}{7}$.

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