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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
If $6 \sin ^{-1}\left(x^2-6 x+8.5\right)=\pi$, then $x$ is equal to
  • A
    1
  • ✓
    2
  • C
    3
  • D
    8
✓

Answer

Correct option: B.
2
(b) : We have, $6 \sin ^{-1}\left(x^2-6 x+8.5\right)=\pi$
$
\Rightarrow \sin ^{-1}\left(x^2-6 x+8.5\right)=\frac{\pi}{6}
$
$\begin{array}{l}\Rightarrow x^2-6 x+8.5=\sin \frac{\pi}{6}=\frac{1}{2} \\ \Rightarrow x^2-6 x+8=0 \\ \Rightarrow(x-4)(x-2)=0 \Rightarrow x=4 \text { or } x=2\end{array}$

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