14 sin^2 x + 4 cos 2x = 11 sin 2x - 4; 14sin^2 x+4(cos^2 x - sin^2 x) =11*2 sinx *cos x - 4(sin^2 x+cos^2 x); 14 sin^2 x + 4cos^2 x - 4 sin^2 x = =22 sin x * cos x - 4 sin^2 x - 4 cos^2 x; 14 sin^2 x - 22 sin x * cos x + 8 cos^2 x = 0; 7 sin^2 x - 11 sin x * cos x + 4 cos^2 x = 0; /: cos^2 x ≠ 0; 7 tg^2 x - 11 tg x + 4 = 0; d = 11^2 - 4*7*4= 121 - 112= 9 =3^2; tg x =(11+3) / 14 = 1; ⇒ x = pi/4 + pi*k; k∈z. или tg x =(11-3) /14= 4/7; x = arctg 4/7 + pi*k; k∈z
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