1. The problem is to simplify the expression \( \cos a + \sin a \). 2. There is no direct simplification formula for \( \cos a + \sin a \) alone, but it can be expressed as a single trigonometric function using the identity: $$\cos a + \sin a = \sqrt{2} \sin\left(a + \frac{\pi}{4}\right) = \sqrt{2} \cos\left(a - \frac{\pi}{4}\right)$$ 3. This comes from the sum-to-product formulas and the fact that \( \sin x + \cos x = \sqrt{2} \sin\left(x + \frac{\pi}{4}\right) \) or equivalently \( \sqrt{2} \cos\left(x - \frac{\pi}{4}\right) \). 4. Therefore, the expression \( \cos a + \sin a \) can be rewritten as \( \sqrt{2} \sin\left(a + \frac{\pi}{4}\right) \) or \( \sqrt{2} \cos\left(a - \frac{\pi}{4}\right) \), which might be more useful depending on the context. 5. This is a common technique to combine sine and cosine terms into a single trigonometric function with a phase shift, simplifying analysis or integration.