MCQ
The value of $\sin \left(2 \tan ^{-1}(0.75)\right)$ is equal to
- A0.75
- B1.5
- C0.96
- D$\sin 1.5$
✓
Answer
$
\begin{array}{l}
\text { (c) : Let } 2 \tan ^{-1}(0.75)=\theta \Rightarrow 0.75=\tan \left(\frac{\theta}{2}\right) \\
\therefore \sin \left(2 \tan ^{-1}(0.75)\right) \\
=\sin \theta=\frac{2 \tan \theta / 2}{1+\tan ^2 \theta / 2}=\frac{2 \times 0.75}{1+(0.75)^2}=\frac{1.50}{1.5625}=0.96
\end{array}
$
\begin{array}{l}
\text { (c) : Let } 2 \tan ^{-1}(0.75)=\theta \Rightarrow 0.75=\tan \left(\frac{\theta}{2}\right) \\
\therefore \sin \left(2 \tan ^{-1}(0.75)\right) \\
=\sin \theta=\frac{2 \tan \theta / 2}{1+\tan ^2 \theta / 2}=\frac{2 \times 0.75}{1+(0.75)^2}=\frac{1.50}{1.5625}=0.96
\end{array}
$
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