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Question:

Prove the following: cos(12/13) + sin(3/5) = sin(56/65)

Solution:

sin(cos(12/13) + sin(3/5)) = sin(cos(12/13))cos(sin(3/5)) + cos(cos(12/13))sin(sin(3/5)) = √(169-144)/13 × √(25-9)/5 + (12/13) × (3/5) = 5/13 × 4/5 + 36/65 = 20/65 + 36/65 = 56/65
Hence proved