Question
If sinA = 3/5 and cosB = 12/13, where A and B are in the
first quadrant, find sin(A + B).Solution
We know sin(A + B) = sinA * cosB + cosA * sinB. Given sinA = 3/5, cosA = √(1 - sin²A) = √(1 - (3/5)²) = √(1 - 9/25) = √(16/25) = 4/5. Also, cosB = 12/13, so sinB = √(1 - cos²B) = √(1 - (12/13)²) = √(1 - 144/169) = √(25/169) = 5/13. Now, sin(A + B) = (3/5)(12/13) + (4/5)(5/13) = 36/65 + 20/65 = 56/65.
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