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y*cosx+sinx=1 equation

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Numerical solution:

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The solution

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y*cos(x) + sin(x) = 1
ycos⁡(x)+sin⁡(x)=1y \cos{\left(x \right)} + \sin{\left(x \right)} = 1
Simplify
The graph
Rapid solution [src] 
     pi
x1 = --
     2
x1=π2x_{1} = \frac{\pi}{2} 
           /    /-1 + y\\         /    /-1 + y\\
x2 = - 2*re|atan|------|| - 2*I*im|atan|------||
           \    \1 + y //         \    \1 + y //
x2=−2re⁡(atan⁡(y−1y+1))−2iim⁡(atan⁡(y−1y+1))x_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} 
x2 = -2*re(atan((y - 1)/(y + 1))) - 2*i*im(atan((y - 1)/(y + 1)))
Sum and product of roots [src] 
sum
pi         /    /-1 + y\\         /    /-1 + y\\
-- + - 2*re|atan|------|| - 2*I*im|atan|------||
2          \    \1 + y //         \    \1 + y //
(−2re⁡(atan⁡(y−1y+1))−2iim⁡(atan⁡(y−1y+1)))+π2\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)}\right) + \frac{\pi}{2} 
=
pi       /    /-1 + y\\         /    /-1 + y\\
-- - 2*re|atan|------|| - 2*I*im|atan|------||
2        \    \1 + y //         \    \1 + y //
−2re⁡(atan⁡(y−1y+1))−2iim⁡(atan⁡(y−1y+1))+π2- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} + \frac{\pi}{2} 
product
pi /      /    /-1 + y\\         /    /-1 + y\\\
--*|- 2*re|atan|------|| - 2*I*im|atan|------|||
2  \      \    \1 + y //         \    \1 + y ///
π2(−2re⁡(atan⁡(y−1y+1))−2iim⁡(atan⁡(y−1y+1)))\frac{\pi}{2} \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)}\right) 
=
    /    /    /-1 + y\\     /    /-1 + y\\\
-pi*|I*im|atan|------|| + re|atan|------|||
    \    \    \1 + y //     \    \1 + y ///
−π(re⁡(atan⁡(y−1y+1))+iim⁡(atan⁡(y−1y+1)))- \pi \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)}\right) 
-pi*(i*im(atan((-1 + y)/(1 + y))) + re(atan((-1 + y)/(1 + y))))
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