2cos^ 5x-√2sin (п/2+5x)=0

sin([latex] \frac{ \pi }{2} [/latex]+5x=cos5x[latex] \\ [/latex] tak znachit[latex] \\ [/latex] 2[latex] cos^{2} 5x [/latex]-[latex] \sqrt{2} [/latex]cos5x=0 [latex] \\ [/latex] 2cos5x(cos5x-[latex] \frac{ \sqrt{2} }{2} [/latex])=0[latex] \\ [/latex] cos5x=0[latex] \\ [/latex] cos5x=[latex] \frac{ \sqrt{2} }{2} [/latex] [latex] \\ [/latex] 5x=[latex] \frac{ \pi }{2} + \pi n[/latex] , n €Z [latex] \\ [/latex] x=[latex] \frac{ \pi }{10} +  \frac{\pi n}{10}[/latex] , n €Z [latex] \\ [/latex] 5x=[latex] \frac{ \pi }{4} + \pi n[/latex] , n €Z [latex] \\ [/latex] x=[latex] \frac{ \pi }{40} +  \frac{\pi n}{40}[/latex] , n €Z [latex] \\ [/latex]