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Resolver desigualdades/ cos2xcosx-sin2xsinx>=-1/2

cos2xcosx-sin2xsinx>=-1/2 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
cos(2*x)*cos(x) - sin(2*x)*sin(x) >= -1/2
−sin⁡(x)sin⁡(2x)+cos⁡(x)cos⁡(2x)≥−12- \sin{\left(x \right)} \sin{\left(2 x \right)} + \cos{\left(x \right)} \cos{\left(2 x \right)} \geq - \frac{1}{2} 
-sin(x)*sin(2*x) + cos(x)*cos(2*x) >= -1/2
Solución de la desigualdad en el gráfico
0-100-80-60-40-20204060801002-2
Respuesta rápida [src] 
  /   /                /      /   /2*pi\\                                     \\     /              /      /   ___    /2*pi\      /2*pi\ \                                     \     \\
  |   |                |      |sin|----||      /    _________________________\||     |              |      | \/ 3 *cos|----| + sin|----| |      /    _________________________\|     ||
  |   |                |      |   \ 9  /|      |   /    2/2*pi\      2/2*pi\ |||     |     2*pi     |      |          \ 9  /      \ 9  / |      |   /    2/2*pi\      2/2*pi\ ||     ||
Or|And|0 <= x, x <= -I*|I*atan|---------| + log|  /  cos |----| + sin |----| |||, And|x <= ----, -I*|I*atan|-----------------------------| + log|  /  cos |----| + sin |----| || <= x||
  |   |                |      |   /2*pi\|      \\/       \ 9  /       \ 9  / /||     |      3       |      |     /2*pi\     ___    /2*pi\|      \\/       \ 9  /       \ 9  / /|     ||
  |   |                |      |cos|----||                                     ||     |              |      |- cos|----| + \/ 3 *sin|----||                                     |     ||
  \   \                \      \   \ 9  //                                     //     \              \      \     \ 9  /            \ 9  //                                     /     //
(0≤x∧x≤−i(log⁡(sin⁡2(2π9)+cos⁡2(2π9))+iatan⁡(sin⁡(2π9)cos⁡(2π9))))∨(x≤2π3∧−i(log⁡(sin⁡2(2π9)+cos⁡2(2π9))+iatan⁡(sin⁡(2π9)+3cos⁡(2π9)−cos⁡(2π9)+3sin⁡(2π9)))≤x)\left(0 \leq x \wedge x \leq - i \left(\log{\left(\sqrt{\sin^{2}{\left(\frac{2 \pi}{9} \right)} + \cos^{2}{\left(\frac{2 \pi}{9} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{2 \pi}{9} \right)}}{\cos{\left(\frac{2 \pi}{9} \right)}} \right)}\right)\right) \vee \left(x \leq \frac{2 \pi}{3} \wedge - i \left(\log{\left(\sqrt{\sin^{2}{\left(\frac{2 \pi}{9} \right)} + \cos^{2}{\left(\frac{2 \pi}{9} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{2 \pi}{9} \right)} + \sqrt{3} \cos{\left(\frac{2 \pi}{9} \right)}}{- \cos{\left(\frac{2 \pi}{9} \right)} + \sqrt{3} \sin{\left(\frac{2 \pi}{9} \right)}} \right)}\right) \leq x\right) 
((0 <= x)∧(x <= -i*(i*atan(sin(2*pi/9)/cos(2*pi/9)) + log(sqrt(cos(2*pi/9)^2 + sin(2*pi/9)^2)))))∨((x <= 2*pi/3)∧(-i*(i*atan((sqrt(3)*cos(2*pi/9) + sin(2*pi/9))/(-cos(2*pi/9) + sqrt(3)*sin(2*pi/9))) + log(sqrt(cos(2*pi/9)^2 + sin(2*pi/9)^2))) <= x))
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