Discuss the continuity of `f(x)=sinx-cosx`

Explanation

To discuss the continuity of the function \( f(x) = \sin x - \cos x \), we will follow these steps:

### Step 1: Identify the Components of the Function
The function \( f(x) \) is composed of two parts: \( \sin x \) and \( -\cos x \).

### Step 2: Check the Continuity of Each Component
Both \( \sin x \) and \( \cos x \) are well-known trigonometric functions. It is established that:
- \( \sin x \) is continuous for all \( x \) in the set of real numbers \( \mathbb{R} \).
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