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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths2. inverse trigonometric function1 Mark
MCQ
Let  ${\tan ^{ - 1}}\left( {\tan \frac{{5\pi }}{4}} \right) = \alpha ,{\tan ^{ - 1}}\left( { - \tan \frac{{2\pi }}{3}} \right) = \beta $ Then :-
  • A
    $\alpha > \beta$
  • ✓
    $4 \alpha -3 \beta = 0$
  • C
    $\alpha + \beta = \frac{5 \pi}{12}$
  • D
    None
✓

Answer

Correct option: B.
$4 \alpha -3 \beta = 0$
b
given, $\alpha=\tan ^{-1}\left(\tan \frac{5 \pi}{4}\right)$

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

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

$=\frac{\pi}{4}$

$\Rightarrow 4 \alpha=\pi$

$\beta=\tan ^{-1}\left(-\tan \frac{2 \pi}{3}\right)$

$=\tan ^{-1}\left(-\tan \left(\pi-\frac{\pi}{3}\right)\right)$

$=\tan ^{-1}\left(\tan \left(\frac{\pi}{3}\right)\right)$

$=\frac{\pi}{3}$

$\Rightarrow 3 \beta=\pi \quad \ldots \ldots$

From (1) and (2) we have

$\therefore 4 \alpha=3 \beta$

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