If the relation sin⁻¹x + sin⁻¹y + sin⁻¹z = π holds, then in the identity x⁴ + y⁴ + z⁴ + 4x²y²z² = k(x²y² + y²z² + z²x²), the value of k is:

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2. The equation sin⁻¹x + sin⁻¹y + sin⁻¹z = π implies that x, y, and z are related in such a way that they can be expressed in terms of sine functions that sum to π. This leads to a specific relationship among their powers, resulting in the identity simplifying to a form where k must equal 2 to maintain equality.

If the relation sin⁻¹x + sin⁻¹y + sin⁻¹z = π holds, then in the identity x⁴ + y⁴ + z⁴ + 4x²y²z² = k(x²y² + y²z² + z²x²), the value of k is:

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