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`

Answer 1

\[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right) = \sin\left( 2 \tan^{- 1} 0 . 75 \right)\]
\[ = \sin\left( \sin^{- 1} \frac{2 \times 0 . 75}{1 + \left( 0 . 75 \right)^2} \right)\]
\[ = \sin\left( \sin^{- 1} 0 . 96 \right)\]
\[ = 0 . 96\]

Hence, the correct answer is option (c).