If sin⁻¹(3/5) + cos⁻¹(12/13) = sin⁻¹C, then C equals:
If sin⁻¹(3/5) + cos⁻¹(12/13) = sin⁻¹C, then C equals:
- A. 56/65
- B. 48/65
- C. 16/65
- D. 33/65
Answer: A) 56/65
Explanation: Let α = sin⁻¹(3/5), β = cos⁻¹(12/13). sin α = 3/5, cos α = 4/5. cos β = 12/13, sin β = 5/13. sin(α+β) = sin α cos β + cos α sin β = (3/5)(12/13)+(4/5)(5/13)=36/65+20/65=56/65. So C = 56/65.
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