Question

The value of $sin(2ta{n}^{-1}(0.75))$ is equal to

• A. $0.75$
• B. $1.5$
• C. $0.96$
• D. $sin1.5$

Answer 1

Answer: (C)

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