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Question
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
Options
0.75
1.5
0.96
`sin^-1 1.5`
Solution
\[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right) = \sin\left( 2 \tan^{- 1} 0 . 75 \right)\]
\[ = \sin\left( \sin^{- 1} \frac{2 \times 0 . 75}{1 + \left( 0 . 75 \right)^2} \right)\]
\[ = \sin\left( \sin^{- 1} 0 . 96 \right)\]
\[ = 0 . 96\]
Hence, the correct answer is option (c).
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