[tex]\displaystyle\bf\\2Cos^{2} \frac{x}{2} \Big(1-Sinx\Big)-Cos^{2} x=0\\\\2Cos^{2} \frac{x}{2} \Big(1-Sinx\Big)-\Big(1- Sin^{2} x\Big)=0\\\\2Cos^{2} \frac{x}{2} \Big(1-Sinx\Big)-\Big(1-Sinx\Big)\Big(1+Sinx\Big)=0\\\\\Big(1-Sinx\Big)\Big(\underbrace{2Cos^{2} \frac{x}{2} }_{1+Cosx}-1-Sinx\Big)=0\\\\\Big(1-Sinx\Big)\Big(1+Cosx-1-Sinx\Big)=0\\\\\Big(1-Sinx\Big)\Big(Cosx-Sinx\Big)=0\\\\\\\left[\begin{array}{ccc}1-Sinx=0\\Cosx-Sinx=0\end{array}\right\\\\\\1)\\\\1-Sinx=0\\\\Sinx=1[/tex]
[tex]\displaystyle\bf\\x=\frac{\pi }{2} +2\pi n,n\in Z\\\\2)\\\\Cosx-Sinx=0 \ |:Cosx\neq 0\\\\\frac{Cosx}{Cosx} -\frac{Sinx}{Cosx} =0\\\\1-tgx=0\\\\tgx=1\\\\x=arctg 1+\pi n,n\in Z\\\\x=\frac{\pi }{4} +\pi n,n\in Z\\\\\\Otvet \ : \ \frac{\pi }{2} +2\pi n,n\in Z \ ; \ \frac{\pi }{4} +\pi n,n\in Z[/tex]
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[tex]\displaystyle\bf\\2Cos^{2} \frac{x}{2} \Big(1-Sinx\Big)-Cos^{2} x=0\\\\2Cos^{2} \frac{x}{2} \Big(1-Sinx\Big)-\Big(1- Sin^{2} x\Big)=0\\\\2Cos^{2} \frac{x}{2} \Big(1-Sinx\Big)-\Big(1-Sinx\Big)\Big(1+Sinx\Big)=0\\\\\Big(1-Sinx\Big)\Big(\underbrace{2Cos^{2} \frac{x}{2} }_{1+Cosx}-1-Sinx\Big)=0\\\\\Big(1-Sinx\Big)\Big(1+Cosx-1-Sinx\Big)=0\\\\\Big(1-Sinx\Big)\Big(Cosx-Sinx\Big)=0\\\\\\\left[\begin{array}{ccc}1-Sinx=0\\Cosx-Sinx=0\end{array}\right\\\\\\1)\\\\1-Sinx=0\\\\Sinx=1[/tex]
[tex]\displaystyle\bf\\x=\frac{\pi }{2} +2\pi n,n\in Z\\\\2)\\\\Cosx-Sinx=0 \ |:Cosx\neq 0\\\\\frac{Cosx}{Cosx} -\frac{Sinx}{Cosx} =0\\\\1-tgx=0\\\\tgx=1\\\\x=arctg 1+\pi n,n\in Z\\\\x=\frac{\pi }{4} +\pi n,n\in Z\\\\\\Otvet \ : \ \frac{\pi }{2} +2\pi n,n\in Z \ ; \ \frac{\pi }{4} +\pi n,n\in Z[/tex]