Решите уравнение cos12x=cos6 х +sin6 х

Cos12x=Cos²6x — Sin²6x=(Cos6x — Sin6x) (Cos6x+Sin6x) (Cos6x+Sin6x) (Cos6x — Sin6x — 1)=01) Cos6x+Sin6x=0 ⇔ tg6x=-1 6x=3π/4+πn, n∈Z x=π/8+πn/6, n∈Z2) Cos6x — Sin6x — 1=0 Cos6x — Sin6x=√2 (Cos6x*Cos (π/4) — Sin6x*Sin (π/4)=√2Cos (6x+π/4) √2Cos (6x+π/4)=1Cos (6x+π/4)=√2/26x+π/4=±π/4+2πn, n∈Zx=πn/3 и x=-π/12+πn/3, n∈Z