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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
$\tan ^{-1}\left(\tan \frac{3 \pi}{4}\right)=$
  • A
    $\frac{-\pi}{2}$
  • ✓
    $\frac{-\pi}{4}$
  • C
    $\frac{\pi}{2}$
  • D
    $\frac{\pi}{4}$
✓

Answer

Correct option: B.
$\frac{-\pi}{4}$
(B) $\tan ^{-1}\left(\tan \frac{3 \pi}{4}\right)=\tan ^{-1}\left(\tan \left(\pi-\frac{\pi}{4}\right)\right)$
$=\tan ^{-1}\left(-\tan \frac{\pi}{4}\right)$
$=-\tan ^{-1}\left(\tan \frac{\pi}{4}\right)$
$=-\frac{\pi}{4}$

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