Step 1: Understanding the Concept:
This problem requires identifying a fundamental trigonometric derivative. Finding a function whose derivative is known is the basic definition of an antiderivative or indefinite integral.
Step 2: Key Formula or Approach:
We evaluate the standard differentiation formulas for each of the core trigonometric choices presented in the options:
- $\frac{d}{dx}(\sin x) = \cos x$
- $\frac{d}{dx}(\cos x) = -\sin x$
- $\frac{d}{dx}(\tan x) = \sec^2 x$
Step 3: Detailed Explanation:
Let's check the derivatives of the given options to find which one results exactly in $\cos x$:
- Option (A): The derivative of the standard sine function is $\frac{d}{dx}(\sin x) = \cos x$. This perfectly matches our target derivative condition.
- Option (B): The derivative of $-\sin x$ yields $\frac{d}{dx}(-\sin x) = -\cos x$, which features an incorrect negative sign.
- Option (C): The derivative of $\tan x$ is $\sec^2 x$.
- Option (D): The derivative of $\sec x$ is $\sec x \tan x$.
Therefore, the function that has a derivative equal to $\cos x$ is $\sin x$, making option (A) correct.
Step 4: Final Answer:
The function whose derivative equals $\cos x$ is $\sin x$.