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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
The value of $\sin\big(2\big(\tan^{-1}0.75\big)\big)$ is equal to:
  • A
    $0.75$
  • B
    $1.5$
  • ✓
    $0.96$
  • D
    $\sin ^{-1} 1.5$
✓

Answer

Correct option: C.
$0.96$
$\sin\big(2\big(\tan^{-1}0.75\big)\big)$
$=\sin\big(2\tan^{-1}0.75\big)$
$=\sin\Big(\sin^{-1}\frac{2\times0.75}{1+(0.75)^2}\Big)$
$=\sin\big(\sin^{-1}0.96\big)$
$=0 .96$
Hence, the correct answer is option $(c).$

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