If `a=costheta+isintheta, b=cos phi+isinphi`,find the values of `cos(theta+phi)` and `cos(theta-phi)` in terms of a and b.

Explanation

To solve the problem, we need to find the values of \( \cos(\theta + \phi) \) and \( \cos(\theta - \phi) \) in terms of the complex numbers \( a \) and \( b \), where \( a = \cos \theta + i \sin \theta \) and \( b = \cos \phi + i \sin \phi \).

### Step-by-Step Solution:

1. **Express \( a \) and \( b \) in exponential form**:
\[ a = \cos \theta + i \sin \theta = e^{i\theta} \]
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