25. （2023•崇川区校级开学）已知函数$f(\alpha )=\frac{\sin (\alpha -\frac{\pi }{2})\cos (\frac{3\pi }{2}+\alpha )\tan (2\pi -\alpha )}{\tan (\alpha +\pi )\sin (\alpha +\pi )}$．
（1）化简$f(\alpha )$；
（2）若$f(\alpha )\centerdot f(\alpha +\frac{\pi }{2})=-\frac{1}{8}$，且$\frac{5\pi }{4}\leqslant \alpha \leqslant \frac{3\pi }{2}$，求$f(\alpha )+f(\alpha +\frac{\pi }{2})$的值；
（3）若$f(\alpha +\frac{\pi }{2})=2f(\alpha )$，求$f(\alpha )\centerdot f(\alpha +\frac{\pi }{2})$的值．