Tригонометрично уравнение 16.sin^{6}x + 6cos2x - 3cos4x=4,7

[Гост]

[tex]16.sin^{6 }x + 6cos2x - 3cos4x=4,75[/tex]
Някакви насоки за тази задача?
Благодаря предварително.

[kmitov]

[tex]16(\sin^22x)^3+6\cos 2x - 3(\cos^22x-\sin^22x)=4,75[/tex]
[tex]16(\frac{1-\cos2x}{2})^3+6\cos 2x - 3(2\cos^22x-1)=4,75[/tex]
[tex]16\frac{1-3\cos 2x+3\cos^22x-\cos^32x}{8}+6\cos 2x - 6\cos^22x+3=4,75[/tex]
[tex]2-6\cos 2x+6\cos^22x-2\cos^32x+6\cos 2x - 6\cos^22x+3=4,75[/tex]

[tex]-2\cos^32x+5=4,75[/tex]
[tex]-2\cos^32x=-0,25[/tex]
[tex]-2\cos^32x=-\frac{1}{4}[/tex]
[tex]\cos^32x=\frac{1}{8}[/tex]
[tex]\cos 2x=\frac{1}{2}[/tex]
[tex]2x=\pm\frac{\pi}{3}+2k\pi, \ \ \ k=0,\pm 1, \pm 2, \ldots[/tex]
[tex]x=\pm\frac{\pi}{6}+k\pi, \ \ \ k=0,\pm 1, \pm 2, \ldots[/tex]