Solving 1st Order Circuits: Private Solution & Finding C, D

[asi123]

Ok, let's say I have a first order circuit with i_s = Acos(wt+phase) (like in the pic).
I'm having problem with the private solution, let's say I pick my private solution like this:
i_p = Bcos(wt + phase) = Ccos(wt) + Dsin(wt) (right?)
After I place this i_p in the equation I come up with this:
f[C,D]*cos(wt) + g[C,D]*sin(wt) = Acos(wt+phase) (right?)
Can I say
f[C,D]*cos(wt) + g[C,D]*sin(wt) = Acos(wt)?
I mean, How do I come up with C and D?

10x in advance.

 

[Defennder]

I'm afraid I'm not understanding your question. What is i_p, f[C,D} and g[C,D]?

 

[CEL]

Ok, let's say I have a first order circuit with i_s = Acos(wt+phase) (like in the pic).
I'm having problem with the private solution, let's say I pick my private solution like this:
i_p = Bcos(wt + phase) = Ccos(wt) + Dsin(wt) (right?)
After I place this i_p in the equation I come up with this:
f[C,D]*cos(wt) + g[C,D]*sin(wt) = Acos(wt+phase) (right?)
Can I say
f[C,D]*cos(wt) + g[C,D]*sin(wt) = Acos(wt)?
I mean, How do I come up with C and D?

10x in advance.

You must develop $$Acos(\omega t + \phi) = A_1cos(\omega t) + A_2sin(\omega t)$$

Now, $$f[C,D] = A_1$$ and $$g[C.D] = A_2$$