4sin^2x+cos4x=1 решите плз задачу

Вопрос школьника по предмету Алгебра

4(1 — cos^2x) + 8cos^4x — 8cos^2x + 1 = 1

4 — 4cos^2x + 8cos^4x — 8cos^2x = 0

8cos^4x — 12cos^2x + 4 = 0 /:4

2cos^4x — 3cos^2x + 1 = 0

Пусть cos^2x = t, тогда

2t^2 — 3t + 1 = 0

D = 9 — 8 = 1

t1 = ( 3 + 1)/4 = 1

t2 = ( 3 — 1)/4 = 1/2

cos^2x = 1

cosx = 1

x = 2pik, k ∈Z

cosx = — 1

x = pi + 2pik, k∈Z

cos^2x = 1/2

cosx = √2/2

x = ± arccos (√2/2) + 2pik, k ∈ Z

cosx = — √2/2

x = ± (pi — arccos √2/2) + 2pik, k ∈ Z