Coherent and incoherent addition of waves

If the waves are coherent, then the resultant intensity is given by

I = I₁ + I₂ + 2 √(I₁ I₂ Cos Θ), where Θ is the phase difference between two waves. For the constructive interference the value of Θ = 0°, so that the Cos Θ = 1 and for the destructive interference the value of  Θ = 90°, so that the Cos Θ = 0.

In case of the incoherent sources or waves we can the intensity simply by algebraic method that means I = I₁ + I₂.

Watch the video below for detailed derivation