a)  $2\cos x-3\cos \left( \pi -x \right)+5\sin \left( \dfrac{7\pi }{2}-x \right)+\cot \left( \dfrac{3\pi }{2}-x \right)$

$=2\cos x+3\cos \left( -x \right)+5\sin \left( \dfrac{7\pi }{2}-4\pi -x \right)+\cot \left( \pi +\dfrac{\pi }{2}-x \right)$

$=2\cos x+3\cos x+5\sin \left( \dfrac{-\pi }{2}-x \right)+\cot \left( \dfrac{\pi }{2}-x \right)$

$=5\cos x-5\sin \left( \dfrac{\pi }{2}+x \right)+\tan x$

$=5\cos x-5\sin \left[ \dfrac{\pi }{2}-\left( -x \right) \right]+\tan x$

$=5\cos x-5\cos \left( -x \right)+\tan x$

$=5\cos x-5\cos x+\tan x$

$=\tan x$

b)$\sin \left( x-17\pi  \right).\cos \left( x+\pi  \right).\tan \left( \dfrac{3\pi }{2}-x \right)$

$=\sin \left( x-\pi -16\pi  \right).\left( -\cos x \right).\tan \left( \pi +\dfrac{\pi }{2}-x \right)$

$=\sin \left( x-\pi  \right).\left( -\cos x \right).\tan \left( \dfrac{\pi }{2}-x \right)$

$=-\sin x.\left( -\cos x \right).\cot x$

$=\sin x.\cos x.\dfrac{\cos x}{\sin x}$

$={{\cos }^{2}}x$