Question

Calculate:
$sin\left(2arc\tan 3\right)$

Answer 1

$sin\left(2arctan3\right)=sin\left(2ta{n}^{-1}3\right)$ if$ta{n}^{-1}3=0$

$\Rightarrow tan\theta =3$

$=sin\left(2\theta \right)$

$=\frac{2tan\theta }{1+ta{n}^2\theta }=\frac{2\times 3}{1+9}=\frac{6}{10}=\frac{3}{5}$