4cos^4*x-4cos^2*x+1=0

Введем новую переменную и делаем замену.  [latex] cos^{2}x =t [/latex] [latex]4 t^{2}-4t+1=0[/latex] [latex]D= (-4)^{2}-4*4=16-16=0 [/latex] [latex]t= \frac{4}{8}= \frac{1}{2} [/latex] [latex] cos^{2}x= \frac{1}{2} [/latex] [latex]cosx= \frac{1}{ \sqrt{2} } [/latex] [latex]cosx= -\frac{1}{ \sqrt{2} } [/latex] [latex]x=+- \frac{ \pi }{4}+2 \pi n, n∈Z[/latex] [latex]x=+- \frac{3 \pi }{4}+2 \pi k, k∉ Z [/latex]