If x = sin^(-1)(1/√2), then what is the value of cos^(-1)(x)?

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Q: If x = sin^(-1)(1/√2), then what is the value of cos^(-1)(x)?

Solution: Since x = sin^(-1)(1/√2) = π/4, then cos^(-1)(x) = π/2 - π/4 = π/4.

Steps: 5

Step 1: Understand that sin^(-1)(1/√2) means we are looking for an angle whose sine is 1/√2.
Step 2: Recall that sin(π/4) = 1/√2. Therefore, x = sin^(-1)(1/√2) = π/4.
Step 3: Now we need to find cos^(-1)(x), which means we are looking for an angle whose cosine is x (which we found to be π/4).
Step 4: Use the identity cos^(-1)(x) + sin^(-1)(x) = π/2. Since x = π/4, we can substitute: cos^(-1)(π/4) = π/2 - π/4.
Step 5: Calculate π/2 - π/4, which equals π/4.