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The value of sin⁻¹(12/13) − sin⁻¹(3/5) is equal to:

1. π − sin⁻¹(63/65)
2. π/2 − cos⁻¹(9/65)
3. π − cos⁻¹(33/65)
4. π/2 − sin⁻¹(56/65)

Correct answer: π/2 − sin⁻¹(56/65)

Solution

The expression sin⁻¹(12/13) − sin⁻¹(3/5) can be simplified using the identity sin⁻¹(a) - sin⁻¹(b) = sin⁻¹(a√(1-b²) - b√(1-a²)), which leads to the result π/2 − sin⁻¹(56/65), confirming that this option correctly represents the difference of the two inverse sine values.

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