Question

sin(2arctan(3/4))

Answer 1

\[\sin\left(2\tan^{-1}\left(\frac{3}{4}\right)\right)=2\sin\left(\tan^{-1}\left(\frac{3}{4}\right)\right)\cos\left(\tan^{-1}\left(\frac{3}{4}\right)\right)\]
Let \(\theta=\tan^{-1}\left(\dfrac{3}{4}\right)\), so that \(\tan\theta=\dfrac{3}{4}\).

\[2\sin\left(\tan^{-1}\left(\frac{3}{4}\right)\right)\cos\left(\tan^{-1}\left(\frac{3}{4}\right)\right)=2\times\frac{3}{5}\times\frac{4}{5}=\cdots\]