Yes, you have \(\displaystyle cos(x)= xsin(x)\) so \(\displaystyle x= cot(x)\). There is no "algebraic" way to solve that but you could use some numeric method. For example I note that if \(\displaystyle x= \pi/4\), \(\displaystyle cot(\pi/4)= 1\) which is larger than \(\displaystyle \pi/4= 0.785...\). But if \(\displaystyle x= \pi/2\), \(\displaystyle cot(\pi/2)= 0\) which is smaller than \(\displaystyle x= \pi/2\). There must be an x between \(\displaystyle \pi/4\) and \(\displaystyle \pi/2\) such that \(\displaystyle x= cot(x)\). Where? We don't know but we could try, say, half way between: \(\displaystyle \frac{\pi/4+ \pi/2}{2}= \frac{3\pi}{8}\). \(\displaystyle cot(3\pi/8)= 0.414\) which is smaller than \(\displaystyle \frac{3\pi}{8}= 1.178\). So there must be a solution between \(\displaystyle \frac{3\pi}{8}\) and \(\displaystyle \frac{\pi}{4}\). Again, try half way between, \(\displaystyle \frac{\frac{3\pi}{8}+ \frac{\pi}{4}}{2}= \frac{5\pi}{16}\)