\(\begin{array}{l}
a)\quad y = x\sin x\\
\to y' = (x)'.\sin x + x.(\sin x)'\\
\to y' = \sin x + x\cos x\\
\to \dfrac{y'}{\cos x} = \tan x + x\\
\to \dfrac{y'}{\cos x} - x = \tan x\\
b)\quad y = x\cos x\\
\to y' = (x)'.\cos x + x.(\cos x)'\\
\to y' = \cos x - x\sin x\\
\to \dfrac{y'}{\sin x} = \cot x - x\\
\to \dfrac{y'}{\sin x} + x = \cot x
\end{array}\)