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Sqrt(a)*cosx-2sinx=sqrt(2)+sqrt(2-a) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
  ___                       ___     _______
\/ a *cos(x) - 2*sin(x) = \/ 2  + \/ 2 - a
acos⁡(x)−2sin⁡(x)=2−a+2\sqrt{a} \cos{\left(x \right)} - 2 \sin{\left(x \right)} = \sqrt{2 - a} + \sqrt{2}
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
    /    /              _____________________\\         /    /              _____________________\\         /    /             _____________________\\         /    /             _____________________\\
    |    |       ___   /       ___   _______ ||         |    |       ___   /       ___   _______ ||         |    |      ___   /       ___   _______ ||         |    |      ___   /       ___   _______ ||
    |    |-2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||         |    |-2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||         |    |2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||         |    |2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||
2*re|atan|-----------------------------------|| + 2*I*im|atan|-----------------------------------|| + - 2*re|atan|----------------------------------|| - 2*I*im|atan|----------------------------------||
    |    |       ___     ___     _______     ||         |    |       ___     ___     _______     ||         |    |      ___     ___     _______     ||         |    |      ___     ___     _______     ||
    \    \     \/ 2  + \/ a  + \/ 2 - a      //         \    \     \/ 2  + \/ a  + \/ 2 - a      //         \    \    \/ 2  + \/ a  + \/ 2 - a      //         \    \    \/ 2  + \/ a  + \/ 2 - a      //
(2re⁡(atan⁡(2a−22−a−2a+2−a+2))+2iim⁡(atan⁡(2a−22−a−2a+2−a+2)))+(−2re⁡(atan⁡(2a−22−a+2a+2−a+2))−2iim⁡(atan⁡(2a−22−a+2a+2−a+2)))\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right) 
=
      /    /             _____________________\\       /    /              _____________________\\         /    /             _____________________\\         /    /              _____________________\\
      |    |      ___   /       ___   _______ ||       |    |       ___   /       ___   _______ ||         |    |      ___   /       ___   _______ ||         |    |       ___   /       ___   _______ ||
      |    |2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||       |    |-2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||         |    |2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||         |    |-2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||
- 2*re|atan|----------------------------------|| + 2*re|atan|-----------------------------------|| - 2*I*im|atan|----------------------------------|| + 2*I*im|atan|-----------------------------------||
      |    |      ___     ___     _______     ||       |    |       ___     ___     _______     ||         |    |      ___     ___     _______     ||         |    |       ___     ___     _______     ||
      \    \    \/ 2  + \/ a  + \/ 2 - a      //       \    \     \/ 2  + \/ a  + \/ 2 - a      //         \    \    \/ 2  + \/ a  + \/ 2 - a      //         \    \     \/ 2  + \/ a  + \/ 2 - a      //
2re⁡(atan⁡(2a−22−a−2a+2−a+2))−2re⁡(atan⁡(2a−22−a+2a+2−a+2))+2iim⁡(atan⁡(2a−22−a−2a+2−a+2))−2iim⁡(atan⁡(2a−22−a+2a+2−a+2))2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} 
producto
/    /    /              _____________________\\         /    /              _____________________\\\ /      /    /             _____________________\\         /    /             _____________________\\\
|    |    |       ___   /       ___   _______ ||         |    |       ___   /       ___   _______ ||| |      |    |      ___   /       ___   _______ ||         |    |      ___   /       ___   _______ |||
|    |    |-2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||         |    |-2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||| |      |    |2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||         |    |2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  |||
|2*re|atan|-----------------------------------|| + 2*I*im|atan|-----------------------------------|||*|- 2*re|atan|----------------------------------|| - 2*I*im|atan|----------------------------------|||
|    |    |       ___     ___     _______     ||         |    |       ___     ___     _______     ||| |      |    |      ___     ___     _______     ||         |    |      ___     ___     _______     |||
\    \    \     \/ 2  + \/ a  + \/ 2 - a      //         \    \     \/ 2  + \/ a  + \/ 2 - a      /// \      \    \    \/ 2  + \/ a  + \/ 2 - a      //         \    \    \/ 2  + \/ a  + \/ 2 - a      ///
(2re⁡(atan⁡(2a−22−a−2a+2−a+2))+2iim⁡(atan⁡(2a−22−a−2a+2−a+2)))(−2re⁡(atan⁡(2a−22−a+2a+2−a+2))−2iim⁡(atan⁡(2a−22−a+2a+2−a+2)))\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right) 
=
   /    /    /              _____________________\\     /    /              _____________________\\\ /    /    /             _____________________\\     /    /             _____________________\\\
   |    |    |       ___   /       ___   _______ ||     |    |       ___   /       ___   _______ ||| |    |    |      ___   /       ___   _______ ||     |    |      ___   /       ___   _______ |||
   |    |    |-2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||     |    |-2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||| |    |    |2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||     |    |2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  |||
-4*|I*im|atan|-----------------------------------|| + re|atan|-----------------------------------|||*|I*im|atan|----------------------------------|| + re|atan|----------------------------------|||
   |    |    |       ___     ___     _______     ||     |    |       ___     ___     _______     ||| |    |    |      ___     ___     _______     ||     |    |      ___     ___     _______     |||
   \    \    \     \/ 2  + \/ a  + \/ 2 - a      //     \    \     \/ 2  + \/ a  + \/ 2 - a      /// \    \    \    \/ 2  + \/ a  + \/ 2 - a      //     \    \    \/ 2  + \/ a  + \/ 2 - a      ///
−4(re⁡(atan⁡(2a−22−a−2a+2−a+2))+iim⁡(atan⁡(2a−22−a−2a+2−a+2)))(re⁡(atan⁡(2a−22−a+2a+2−a+2))+iim⁡(atan⁡(2a−22−a+2a+2−a+2)))- 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right) 
-4*(i*im(atan((-2 + sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)))/(sqrt(2) + sqrt(a) + sqrt(2 - a)))) + re(atan((-2 + sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)))/(sqrt(2) + sqrt(a) + sqrt(2 - a)))))*(i*im(atan((2 + sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)))/(sqrt(2) + sqrt(a) + sqrt(2 - a)))) + re(atan((2 + sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)))/(sqrt(2) + sqrt(a) + sqrt(2 - a)))))
Respuesta rápida [src] 
         /    /              _____________________\\         /    /              _____________________\\
         |    |       ___   /       ___   _______ ||         |    |       ___   /       ___   _______ ||
         |    |-2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||         |    |-2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||
x1 = 2*re|atan|-----------------------------------|| + 2*I*im|atan|-----------------------------------||
         |    |       ___     ___     _______     ||         |    |       ___     ___     _______     ||
         \    \     \/ 2  + \/ a  + \/ 2 - a      //         \    \     \/ 2  + \/ a  + \/ 2 - a      //
x1=2re⁡(atan⁡(2a−22−a−2a+2−a+2))+2iim⁡(atan⁡(2a−22−a−2a+2−a+2))x_{1} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} 
           /    /             _____________________\\         /    /             _____________________\\
           |    |      ___   /       ___   _______ ||         |    |      ___   /       ___   _______ ||
           |    |2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||         |    |2 + \/ 2 *\/  a - \/ 2 *\/ 2 - a  ||
x2 = - 2*re|atan|----------------------------------|| - 2*I*im|atan|----------------------------------||
           |    |      ___     ___     _______     ||         |    |      ___     ___     _______     ||
           \    \    \/ 2  + \/ a  + \/ 2 - a      //         \    \    \/ 2  + \/ a  + \/ 2 - a      //
x2=−2re⁡(atan⁡(2a−22−a+2a+2−a+2))−2iim⁡(atan⁡(2a−22−a+2a+2−a+2))x_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} 
x2 = -2*re(atan((sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)) + 2)/(sqrt(a) + sqrt(2 - a) + sqrt(2)))) - 2*i*im(atan((sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)) + 2)/(sqrt(a) + sqrt(2 - a) + sqrt(2))))
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