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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
If $\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1$, then $x$ is equal to
  • A
    1
  • B
    $0$
  • C
    $\frac{4}{5}$
  • ✓
    $\frac{1}{5}$
✓

Answer

Correct option: D.
$\frac{1}{5}$
(D) $\sin ^{-1} \frac{1}{5}+\cos ^{-1} x=\frac{\pi}{2}$
$\begin{array}{l}\therefore \sin ^{-1} \frac{1}{5}=\frac{\pi}{2}-\cos ^{-1} x=\sin ^{-1} x \\ \therefore x=\frac{1}{5}\end{array}$

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