Discuss the continuity of the following functions:
(a) `f(x) = sin x + cos x`
(b) `f(x) = sin x - cos x`
(c) `f(x) = sin x . cos x`

Explanation

To discuss the continuity of the given functions, we will analyze each function step by step.

### (a) \( f(x) = \sin x + \cos x \)

1. **Identify the components**: The function \( f(x) \) is the sum of two functions: \( p(x) = \sin x \) and \( q(x) = \cos x \).

2. **Check continuity of \( p(x) \)**: The sine function, \( \sin x \), is continuous for all real numbers.

...