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2sinx-(sinx)^2=(cosx)^3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
              2         3   
2*sin(x) - sin (x) = cos (x)
$$- \sin^{2}{\left(x \right)} + 2 \sin{\left(x \right)} = \cos^{3}{\left(x \right)}$$
Gráfica
Suma y producto de raíces [src]
suma
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2*atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 0// + 2*atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 1// + 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 2/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 2/// + 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 3/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 3/// + 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 4/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 4/// + 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 5/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 5///
$$\left(\left(\left(\left(2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 0\right)} \right)} + 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 1\right)} \right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 2\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 2\right)} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 3\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 3\right)} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 4\right)} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 5\right)} \right)}\right)}\right)$$
=
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2*atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 0// + 2*atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 1// + 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 2/// + 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 3/// + 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 4/// + 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 5/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 2/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 3/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 4/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 5///
$$2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 0\right)} \right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 2\right)} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 3\right)} \right)}\right)} + 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 1\right)} \right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 4\right)} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 2\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 3\right)} \right)}\right)}$$
producto
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2*atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 0//*2*atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 1//*\2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 2/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 2////*\2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 3/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 3////*\2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 4/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 4////*\2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 5/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 5////
$$2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 0\right)} \right)} 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 1\right)} \right)} \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 2\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 2\right)} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 3\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 3\right)} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 4\right)} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 5\right)} \right)}\right)}\right)$$
=
   /    /    /       / 6      5      4      3    2             \\\     /    /       / 6      5      4      3    2             \\\\ /    /    /       / 6      5      4      3    2             \\\     /    /       / 6      5      4      3    2             \\\\ /    /    /       / 6      5      4      3    2             \\\     /    /       / 6      5      4      3    2             \\\\ /    /    /       / 6      5      4      3    2             \\\     /    /       / 6      5      4      3    2             \\\\     /       / 6      5      4      3    2             \\     /       / 6      5      4      3    2             \\
64*\I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 2/// + re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 2////*\I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 3/// + re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 3////*\I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 4/// + re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 4////*\I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 5/// + re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 5////*atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 0//*atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 1//
$$64 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 2\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 2\right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 3\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 3\right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 4\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 4\right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 5\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 5\right)} \right)}\right)}\right) \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 0\right)} \right)} \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 1\right)} \right)}$$
64*(i*im(atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 2))) + re(atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 2))))*(i*im(atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 3))) + re(atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 3))))*(i*im(atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 4))) + re(atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 4))))*(i*im(atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 5))) + re(atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 5))))*atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 0))*atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 1))
Respuesta rápida [src]
           /       / 6      5      4      3    2             \\
x1 = 2*atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 0//
$$x_{1} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 0\right)} \right)}$$
           /       / 6      5      4      3    2             \\
x2 = 2*atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 1//
$$x_{2} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 1\right)} \right)}$$
         /    /       / 6      5      4      3    2             \\\         /    /       / 6      5      4      3    2             \\\
x3 = 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 2/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 2///
$$x_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 2\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 2\right)} \right)}\right)}$$
         /    /       / 6      5      4      3    2             \\\         /    /       / 6      5      4      3    2             \\\
x4 = 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 3/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 3///
$$x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 3\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 3\right)} \right)}\right)}$$
         /    /       / 6      5      4      3    2             \\\         /    /       / 6      5      4      3    2             \\\
x5 = 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 4/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 4///
$$x_{5} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 4\right)} \right)}\right)}$$
         /    /       / 6      5      4      3    2             \\\         /    /       / 6      5      4      3    2             \\\
x6 = 2*re\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 5/// + 2*I*im\atan\CRootOf\x  + 4*x  - 7*x  + 8*x  - x  + 4*x - 1, 5///
$$x_{6} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} + 4 x^{5} - 7 x^{4} + 8 x^{3} - x^{2} + 4 x - 1, 5\right)} \right)}\right)}$$
Eq(x6, 2*re(atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 5))) + 2*i*im(atan(CRootOf(x^6 + 4*x^5 - 7*x^4 + 8*x^3 - x^2 + 4*x - 1, 5))))
Respuesta numérica [src]
x1 = 6.7570985097032
x2 = -15.3505376943517
x3 = 3.49901822718708
x4 = -40.48327892307
x5 = -84.4655760733271
x6 = -68.6411251764518
x7 = -144.039348862607
x8 = -56.0747545620927
x9 = -43.5083839477335
x10 = -37.2251986405539
x11 = -2.78416707999251
x12 = -27.9169083087109
x13 = -81.207495790811
x14 = 97.7467978348809
x15 = 22.3485741487258
x16 = 63.3057662743195
x17 = -18.3756427190151
x18 = 91.4636125277013
x19 = -46.7664642302496
x20 = -93.7738664051702
x21 = 53.7645006846238
x22 = -34.2000936158904
x23 = -71.899205458968
x24 = 47.4813153774442
x25 = -74.9243104836314
x26 = -90.7487613805067
x27 = 25.606654431242
x28 = 44.4562103527807
x29 = -169.172090091325
x30 = -332.534908077994
x31 = -62.3579398692723
x32 = -49.7915692549131
x33 = 72.6140566061625
x34 = 28.6317594559054
x35 = 0.473913202523613
x36 = 75.8721368886787
x37 = -24.6588280261947
x38 = 364.89866101894
x39 = -78.1823907661475
x40 = 19.3234691240624
x41 = 31.8898397384215
x42 = -21.6337230015313
x43 = 9.78220353436666
x44 = -30.9420133333743
x45 = 50.7393956599603
x46 = -59.3328348446088
x47 = -65.6160201517884
x48 = 94.7216928102174
x49 = -100.05705171235
x50 = 38.1730250456011
x51 = 34.914944763085
x52 = -12.0924574118356
x53 = 13.0402838168828
x54 = 60.0476859918034
x55 = 66.3308712989829
x56 = 88.4385075030378
x57 = -87.4906810979906
x58 = 101.004878117397
x59 = 16.0653888415462
x60 = 57.0225809671399
x61 = 82.1553221958582
x62 = 69.5889515814991
x63 = -5.80927210465597
x63 = -5.80927210465597