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INVERSE TRIGNOMETRIC FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINVERSE TRIGNOMETRIC FUNCTIONS1 Mark
Question
Choose the correct answer from the given four options.
The value of $\sin\big[2\tan^{-1}(0.75)\big]$ is equal to:
  1. 0.75
  2. 1.5
  3. 0.96
  4. sin1.5
✓

Answer

  1. 0.96

Solution:

We have, $\sin\big[2\tan^{-1}(0.75)\big]$

$=\sin\Big(2\tan^{-1}\frac{3}{4}\Big)$

$=\sin\Bigg(\sin^{-1}\frac{2.\frac{3}{4}}{1+\frac{9}{16}}\Bigg)$

$\Big(\because\ 2\tan^{-1}\text{x}=\sin^{-1}\frac{2\text{x}}{1+\text{x}^2}\Big)$

$=\sin\Bigg(\sin^{-1}\frac{\frac{3}{2}}{\frac{25}{16}}\Bigg)$

$=\sin\Big(\sin^{-1}\frac{24}{25}\Big)=\frac{24}{25}=0.96$

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