$Theequation(\cos p-1)x^2+\left(\cos p\right)x+\sin p=0hasrealroots,then\text{'}p\text{'}cantakeanyvalueinthe\mathrm{int}erval$

$\begin{array}{l}GivenEquation(\cos p-1)x^2+\left(\cos p\right)x+\sin p=0hasrealroots\\ thenD\ge 0\Rightarrow b^2-4ac\ge 0\\ \Rightarrow {\cos }^{2}p-4(\cos p-1)\sin p\ge 0\\ \Rightarrow {\cos }^{2}p-4\cos p.\sin p+4\sin p\ge 0\\ \Rightarrow {(\cos p-2\sin p)}^2-4{\sin }^{2}p+4\sin p\ge 0\\ \Rightarrow {(\cos p-2\sin p)}^2+4\sin p(1-\sin p)\ge 0\\ \therefore {(\cos p-2\sin p)}^2\ge 0,1\forall valuesofp\\ \therefore 1-\sin p\ge 0forp\in (0,\pi )\end{array}$