# Using Manipulate for solving equations

I want to solve one easy equation with two parameters which changes. I tried to use Manipulate for see the solution "in real time" after each changing one or two of two parameters. But i have next message in result window "Null". So my code is below:

Options[Simple] = {
Сut1 -> 0,
Сut2 -> 0
};
Simple[
OptionsPattern[]
] := Module[
{
kit1 = OptionValue[Сut1],
kit2 = OptionValue[Сut2]
},
solution = N[-Cos[kit1]^2 + 4 Cos[kit1]^2*Sin[kit1]^2*Cos[kit2]^2 - 1.5
Sin[kit2]^8*(0.3 + Sin[kit1]^2*Cos[kit2]^2) - 0.5*Sin[kit2]*Sin[kit1]];
]

solution1 = Manipulate[Module[{rmt1 = Simple[Сut1 -> kyts1, Сut2 -> kyts2]},
rmt1], "Select Options:",
"Value of θ0 angle:", {{kyts1, 90.0, "Degree"}, 0.0, 270.0},
"Value of ϕ0 angle:", {{kyts2, 45.0, "Degree"}, 0.0, 270.0},
"Result is:"];


The last ; before the closing bracket for the Module in your definition of Simple is effectively suppressing your output. For the same reason, you should NOT have a ; after the closing bracket of the Manipulate expression. If you remove those, values will be displayed.

As a side note, your user-selected degree values are currently interpreted as radians; you may want to modify your call to Simple within the Manipulate to Simple[Cut1 -> kyts1 Degree, Cut2 -> kyts2 Degree].

In addition to those changes, a few other things struck me as odd in your code, so I propose the following refactoring:

ClearAll[Simple]

Options[Simple] = {Сut1 -> 0, Сut2 -> 0};

Simple[OptionsPattern[]] := Module[
{kit1 = OptionValue[Сut1], kit2 = OptionValue[Сut2]},
N[-Cos[kit1]^2 + 4 Cos[kit1]^2*Sin[kit1]^2*Cos[kit2]^2 -
1.5 Sin[kit2]^8*(0.3 + Sin[kit1]^2*Cos[kit2]^2) - 0.5*Sin[kit2]*Sin[kit1]]
]

Manipulate[
Simple[Сut1 -> kyts1 Degree, Сut2 -> kyts2 Degree],
"Select Options:",
"Value of θ0 angle:", {{kyts1, 90.0, "Degree"}, 0.0, 270.0, Appearance -> "Labeled"},
"Value of ϕ0 angle:", {{kyts2, 45.0, "Degree"}, 0.0, 270.0, Appearance -> "Labeled"},
"Result is:"
]