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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
$\sin ^{-1} x+\sin ^{-1} \frac{1}{x}+\cos ^{-1} x+\cos ^{-1} \frac{1}{x}=$
  • ✓
    $\pi$
  • B
    $\frac{\pi}{2}$
  • C
    $\frac{3 \pi}{2}$
  • D
    $\frac{2 \pi}{3}$
✓

Answer

Correct option: A.
$\pi$
(A) $\sin ^{-1} x+\sin ^{-1} \frac{1}{x}+\cos ^{-1} x+\cos ^{-1} \frac{1}{x}$
$=\left\{\sin ^{-1}(x)+\cos ^{-1}(x)\right\}+\left\{\sin ^{-1}\left(\frac{1}{x}\right)+\cos ^{-1}\left(\frac{1}{x}\right)\right\}$
$=\frac{\pi}{2}+\frac{\pi}{2}=\pi$

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