# How do you find the exact value for sin (tan^-1 (3/4))?

$= \sin \left({\tan}^{-} 1 \left(\frac{3}{4}\right)\right) = \sin \left({\cot}^{-} 1 \left(\frac{4}{3}\right)\right) = \sin \left({\csc}^{-} 1 \sqrt{1 + {\left(\frac{4}{3}\right)}^{2}}\right)$
$= \sin \left({\csc}^{-} 1 \left(\frac{5}{3}\right)\right) = \sin \left({\sin}^{-} 1 \left(\frac{3}{5}\right)\right) = \frac{3}{5}$