Решить?

1+4cosx=cos2x

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)