1+4cos x = cos 2x
1+4cos x = 2*cos^2 (x) - 1 // т.к. cos 2x = 2*cos x -1
2+4cos x = 2*cos^2 (x) // разделим все на два
1+2cos x = cos^2 (x)
cos^2(x) - 2cos x -1 =0
a = cos x a^2 = cos^2 (x)
a^2-2a-1 = 0
D=4+4=0
a1=(2+2*2^(1/2))/2=1+2^(1/2)=cos x
a2=(2-2*2^(1/2))/2=1-2^(1/2)= cos x
cos x = 1-2^(1/2) cos x = 1+2^(1/2)
x = π*n + arccos (1-2^(1/2) x = π*n + arccos (1+2^(1/2)
PS
^ - знак степени(если что)