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How many solutions exist for the equation arcsin(x) + arccos(y) = π/2?

1. None
2. One
3. Two
4. Infinite

Correct answer: Infinite

Solution

Since arccos(y)=pi/2-arcsin(x)=arccos(x), the equation forces y=x for every x in [-1,1], giving infinitely many solutions. The correct option is 'Infinite', not 'Two'.

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