Proposition: Zero of Cosine
The cosine function has in the closed interval $[0,2]$ exactly one zero at $\pi/2.$ Formally, there exists exactly one $\alpha\in[0,2]$ with $\cos(\alpha)=0,$ and we have $\alpha=\pi/2.$
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983