i need to prove that for every $\displaystyle y\geq x\geq\frac{3}{\pi} $ :$\displaystyle y^{2}cos\frac{1}{y}-x^{2}cos\frac{1}{x}\geq(y^{2}-x^{2})cos\frac{1}{x}\geq\frac{(y^{2}-x^{2})}{2}$