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Question:

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

π - sin⁻¹(63/65)

π - cos⁻¹(33/65)

π/2 - sin⁻¹(56/65)

π/2 - cos⁻¹(9/65)

Solution:

Correct option is C. π/2 - sin⁻¹(56/65)
sin⁻¹(12/13) - sin⁻¹(3/5)
sin⁻¹(x₁y₂ - y₁x₂/√(x₁² + y₁²)√(x₂² + y₂²))=sin⁻¹(33/65)=cos⁻¹(56/65)=π/2 - sin⁻¹(56/65).