If sin^-1x + sin^-1y = π/2, then cos^-1x + cos^-1y is equal to

• A: π/2
• B: π/4
• C: π
• D: 3π/4

To solve the equation sin^-1x + sin^-1y = π/2, we can use a trigonometric identity. The identity states that if sin^-1x + sin^-1y = π/2, then it implies that x and y are related through cosine.

Understanding the Relationship

From the equation, we can deduce that:

• sin^-1x = π/2 - sin^-1y
• This means that cos(sin^-1y) = x and cos(sin^-1x) = y.

Finding cos^-1x + cos^-1y

Using the identity for cosine, we know:

• cos^-1x = sin^-1(√(1 - x²))
• cos^-1y = sin^-1(√(1 - y²))

Since sin^-1x + sin^-1y = π/2, we can conclude that:

• cos^-1x + cos^-1y = π/2.

Final Answer

Thus, the value of cos^-1x + cos^-1y is equal to π/2. Therefore, the correct option is A: π/2.