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(1-6*(sin(x))^2)^2<24*(sin(x))^2 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
               2             
/         2   \          2   
\1 - 6*sin (x)/  < 24*sin (x)
$$\left(1 - 6 \sin^{2}{\left(x \right)}\right)^{2} < 24 \sin^{2}{\left(x \right)}$$
(1 - 6*sin(x)^2)^2 < 24*sin(x)^2
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
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$$x < - i \left(\log{\left(\sqrt{\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \right)}}{2} \right)} + \sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \right)}}{2} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \right)}}{2} \right)}} \right)}\right) \wedge - i \left(\log{\left(\sqrt{\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \right)}}{2} \right)} + \sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \right)}}{2} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{4 \sqrt{2}}{7} \right)}}{2} \right)}} \right)}}{2} \right)}} \right)}\right) < x$$
(x < -i*(i*atan(cos(atan(sin(atan(4*sqrt(2)/7)/2)/cos(atan(4*sqrt(2)/7)/2))/2)/sin(atan(sin(atan(4*sqrt(2)/7)/2)/cos(atan(4*sqrt(2)/7)/2))/2)) + log(sqrt(sqrt(cos(atan(4*sqrt(2)/7)/2)^2 + sin(atan(4*sqrt(2)/7)/2)^2)*cos(atan(sin(atan(4*sqrt(2)/7)/2)/cos(atan(4*sqrt(2)/7)/2))/2)^2 + sqrt(cos(atan(4*sqrt(2)/7)/2)^2 + sin(atan(4*sqrt(2)/7)/2)^2)*sin(atan(sin(atan(4*sqrt(2)/7)/2)/cos(atan(4*sqrt(2)/7)/2))/2)^2))))∧(-i*(i*atan(sin(atan(sin(atan(4*sqrt(2)/7)/2)/cos(atan(4*sqrt(2)/7)/2))/2)/cos(atan(sin(atan(4*sqrt(2)/7)/2)/cos(atan(4*sqrt(2)/7)/2))/2)) + log(sqrt(sqrt(cos(atan(4*sqrt(2)/7)/2)^2 + sin(atan(4*sqrt(2)/7)/2)^2)*cos(atan(sin(atan(4*sqrt(2)/7)/2)/cos(atan(4*sqrt(2)/7)/2))/2)^2 + sqrt(cos(atan(4*sqrt(2)/7)/2)^2 + sin(atan(4*sqrt(2)/7)/2)^2)*sin(atan(sin(atan(4*sqrt(2)/7)/2)/cos(atan(4*sqrt(2)/7)/2))/2)^2))) < x)