The value of (2 ^ -1 (0.75) ) is equal to - Vidyadip

MCQ

The value of $\sin \left(2 \tan ^{-1}(0.75)\right)$ is equal to

A
$0.75$
B
$1.5$
✓
$0.96$
D
$\sin 1.5$

✓

Answer

Correct option: C.

$0.96$

Let $2 \tan ^{-1}(0.75)=\theta$
$\Rightarrow 0.75=\tan \left(\frac{\theta}{2}\right)$
$\therefore \sin \left(2 \tan ^{-1}(0.75)\right)$
$=\sin \theta=\frac{2 \tan \theta / 2}{1+\tan ^2 \theta / 2}=\frac{2 \times 0.75}{1+(0.75)^2}=\frac{1.50}{1.5625}=0.96$

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