Solve the following equation $\cos\big(\tan^{-1}x\big)=\sin\bigg(\cot^{-1}{\frac{3}{4}}\bigg)$

Question

$\begin{array}{1 1} \frac{4}{3} \\ \pm \frac{3}{4} \\ \frac{4}{5} \\ \frac{3}{5} \end{array}$