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1+sin2(x)/sin(x)+cos(x)+1=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
       2                    
    sin (x)                 
1 + ------- + cos(x) + 1 = 0
     sin(x)
((1+sin⁡2(x)sin⁡(x))+cos⁡(x))+1=0\left(\left(1 + \frac{\sin^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) + \cos{\left(x \right)}\right) + 1 = 0
Simplificar
Gráfica
0-80-60-40-2020406080-10010005
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
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- 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 // + - 2*re\atan\1 + I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 //
(−2re⁡(atan⁡(1+2i))−2iim⁡(atan⁡(1+2i)))+(−2re⁡(atan⁡(1−2i))−2iim⁡(atan⁡(1−2i)))\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) 
=
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- 2*re\atan\1 + I*\/ 2 // - 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 //
−2re⁡(atan⁡(1+2i))−2re⁡(atan⁡(1−2i))−2iim⁡(atan⁡(1+2i))−2iim⁡(atan⁡(1−2i))- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} 
producto
/      /    /        ___\\         /    /        ___\\\ /      /    /        ___\\         /    /        ___\\\
\- 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 ///*\- 2*re\atan\1 + I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 ///
(−2re⁡(atan⁡(1−2i))−2iim⁡(atan⁡(1−2i)))(−2re⁡(atan⁡(1+2i))−2iim⁡(atan⁡(1+2i)))\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right) 
=
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4*\I*im\atan\1 + I*\/ 2 // + re\atan\1 + I*\/ 2 ///*\I*im\atan\1 - I*\/ 2 // + re\atan\1 - I*\/ 2 ///
4(re⁡(atan⁡(1−2i))+iim⁡(atan⁡(1−2i)))(re⁡(atan⁡(1+2i))+iim⁡(atan⁡(1+2i)))4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right) 
4*(i*im(atan(1 + i*sqrt(2))) + re(atan(1 + i*sqrt(2))))*(i*im(atan(1 - i*sqrt(2))) + re(atan(1 - i*sqrt(2))))
Respuesta rápida [src] 
           /    /        ___\\         /    /        ___\\
x1 = - 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 //
x1=−2re⁡(atan⁡(1−2i))−2iim⁡(atan⁡(1−2i))x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} 
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x2 = - 2*re\atan\1 + I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 //
x2=−2re⁡(atan⁡(1+2i))−2iim⁡(atan⁡(1+2i))x_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} 
x2 = -2*re(atan(1 + sqrt(2)*i)) - 2*i*im(atan(1 + sqrt(2)*i))
Respuesta numérica [src] 
x1 = -2.35619449019234 + 0.881373587019543*i
x2 = -2.35619449019234 - 0.881373587019543*i
x2 = -2.35619449019234 - 0.881373587019543*i
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