cos2x + sin2x = 1/2 / домножим на 2
2cos2x + 2sin2x — 1 = 0
2(cos^2x — sin^2x) + 4sinxcosx — (sin^2x + cos^2x) = 0
2cos^2x — 2sin^2x + 4sinxcosx — sin^2x — cos^2x = 0
— 3sin^2x + 4sinxcosx + cos^2x = 0 / делим на минус 1
3sin^2x — 4sincosx — cos^2x = 0 / делим на cos^2x ≠ 0
3tg^2x — 4tgx — 1 = 0
Замена tgx = t
3t^2 — 4t — 1 = 0
D = 16 + 12 = 28
t1 = ( 4 +2√7)/6 = (2 + √7)/3
t1 = ( 4 — 2√7)/6 = (2 — √7)/3x = arctg (2+√7)/3 + pik
x = arctg ( 2 -√7)/3 + pik