Evaluate the expression sin^(-1)(x) + cos^(-1)(x).

Evaluate the expression sin^(-1)(x) + cos^(-1)(x).

Step 1: Understand the functions involved. sin^(-1)(x) is the inverse sine function, also known as arcsin(x), and cos^(-1)(x) is the inverse cosine function, also known as arccos(x).
Step 2: Recall the definitions of these functions. The arcsin(x) gives you an angle whose sine is x, and arccos(x) gives you an angle whose cosine is x.
Step 3: Recognize the relationship between sine and cosine. For any angle θ, sin(θ) and cos(θ) are related by the identity sin(θ) = cos(π/2 - θ).
Step 4: Use the relationship to find the sum. If θ = sin^(-1)(x), then cos^(-1)(x) is the angle that complements θ to π/2. Therefore, sin^(-1)(x) + cos^(-1)(x) = π/2.
Step 5: Note the domain. This relationship holds true for all x in the range [-1, 1], which is the domain of the arcsin and arccos functions.

Inverse Trigonometric Functions – The relationship between the inverse sine and inverse cosine functions, specifically that their sum equals π/2.
Domain of Functions – Understanding the valid input range for the functions involved, which is [-1, 1] for both sin^(-1)(x) and cos^(-1)(x).