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(a-2)*sin(x)+cos(x)=a la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
(a - 2)*sin(x) + cos(x) = a
(a−2)sin⁡(x)+cos⁡(x)=a\left(a - 2\right) \sin{\left(x \right)} + \cos{\left(x \right)} = a
Simplificar
Gráfica
Respuesta rápida [src] 
           /    /      _________    \\         /    /      _________    \\
           |    |2 + \/ 5 - 4*a  - a||         |    |2 + \/ 5 - 4*a  - a||
x1 = - 2*re|atan|-------------------|| - 2*I*im|atan|-------------------||
           \    \       1 + a       //         \    \       1 + a       //
x1=−2re⁡(atan⁡(−a+5−4a+2a+1))−2iim⁡(atan⁡(−a+5−4a+2a+1))x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} 
         /    /           _________\\         /    /           _________\\
         |    |-2 + a + \/ 5 - 4*a ||         |    |-2 + a + \/ 5 - 4*a ||
x2 = 2*re|atan|--------------------|| + 2*I*im|atan|--------------------||
         \    \       1 + a        //         \    \       1 + a        //
x2=2re⁡(atan⁡(a+5−4a−2a+1))+2iim⁡(atan⁡(a+5−4a−2a+1))x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} 
x2 = 2*re(atan((a + sqrt(5 - 4*a) - 2)/(a + 1))) + 2*i*im(atan((a + sqrt(5 - 4*a) - 2)/(a + 1)))
Suma y producto de raíces [src] 
suma
      /    /      _________    \\         /    /      _________    \\       /    /           _________\\         /    /           _________\\
      |    |2 + \/ 5 - 4*a  - a||         |    |2 + \/ 5 - 4*a  - a||       |    |-2 + a + \/ 5 - 4*a ||         |    |-2 + a + \/ 5 - 4*a ||
- 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|| + 2*re|atan|--------------------|| + 2*I*im|atan|--------------------||
      \    \       1 + a       //         \    \       1 + a       //       \    \       1 + a        //         \    \       1 + a        //
(−2re⁡(atan⁡(−a+5−4a+2a+1))−2iim⁡(atan⁡(−a+5−4a+2a+1)))+(2re⁡(atan⁡(a+5−4a−2a+1))+2iim⁡(atan⁡(a+5−4a−2a+1)))\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)}\right) 
=
      /    /      _________    \\       /    /           _________\\         /    /      _________    \\         /    /           _________\\
      |    |2 + \/ 5 - 4*a  - a||       |    |-2 + a + \/ 5 - 4*a ||         |    |2 + \/ 5 - 4*a  - a||         |    |-2 + a + \/ 5 - 4*a ||
- 2*re|atan|-------------------|| + 2*re|atan|--------------------|| - 2*I*im|atan|-------------------|| + 2*I*im|atan|--------------------||
      \    \       1 + a       //       \    \       1 + a        //         \    \       1 + a       //         \    \       1 + a        //
−2re⁡(atan⁡(−a+5−4a+2a+1))+2re⁡(atan⁡(a+5−4a−2a+1))−2iim⁡(atan⁡(−a+5−4a+2a+1))+2iim⁡(atan⁡(a+5−4a−2a+1))- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} 
producto
/      /    /      _________    \\         /    /      _________    \\\ /    /    /           _________\\         /    /           _________\\\
|      |    |2 + \/ 5 - 4*a  - a||         |    |2 + \/ 5 - 4*a  - a||| |    |    |-2 + a + \/ 5 - 4*a ||         |    |-2 + a + \/ 5 - 4*a |||
|- 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|||*|2*re|atan|--------------------|| + 2*I*im|atan|--------------------|||
\      \    \       1 + a       //         \    \       1 + a       /// \    \    \       1 + a        //         \    \       1 + a        ///
(−2re⁡(atan⁡(−a+5−4a+2a+1))−2iim⁡(atan⁡(−a+5−4a+2a+1)))(2re⁡(atan⁡(a+5−4a−2a+1))+2iim⁡(atan⁡(a+5−4a−2a+1)))\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)}\right) 
=
   /    /    /           _________\\     /    /           _________\\\ /    /    /      _________    \\     /    /      _________    \\\
   |    |    |-2 + a + \/ 5 - 4*a ||     |    |-2 + a + \/ 5 - 4*a ||| |    |    |2 + \/ 5 - 4*a  - a||     |    |2 + \/ 5 - 4*a  - a|||
-4*|I*im|atan|--------------------|| + re|atan|--------------------|||*|I*im|atan|-------------------|| + re|atan|-------------------|||
   \    \    \       1 + a        //     \    \       1 + a        /// \    \    \       1 + a       //     \    \       1 + a       ///
−4(re⁡(atan⁡(−a+5−4a+2a+1))+iim⁡(atan⁡(−a+5−4a+2a+1)))(re⁡(atan⁡(a+5−4a−2a+1))+iim⁡(atan⁡(a+5−4a−2a+1)))- 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)}\right) 
-4*(i*im(atan((-2 + a + sqrt(5 - 4*a))/(1 + a))) + re(atan((-2 + a + sqrt(5 - 4*a))/(1 + a))))*(i*im(atan((2 + sqrt(5 - 4*a) - a)/(1 + a))) + re(atan((2 + sqrt(5 - 4*a) - a)/(1 + a))))
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