How to Derive Malus' Law for Two Polarizers Using Integrals?

[Arman777]

Is there any source that how can I derive the Malus of ?
Where there's two polarizer

This is the equation
$$I_{out}=I_{in}[H_{90}+(H_0-H_{90})]cos^2(θ)$$

$H_0=1/2(k_1^2+k_2^2)$ and $H_{90} = k_1k_2$

Also I need to derive the $$I_{out}=1/2I_{in}cos^2θ$$ using integrals

Please help

 

[Arman777]

Are there any additional conditions?

I don't think so no. We made an experiment and in the theory part I need to write the derivation but I couldn't find any source of it. This is the general condiiton I guess ?