If sin A = 8/17 and cos B = 15/17, find sin A cos B + cos A sin B:
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Correct answer: C
Explanation
sin A = 8/17, cos B = 15/17
According to the formula:
sin(A + B) = sin A cos B + cos A sin B
sin²θ + cos²θ = 1
cos A = √(1 − sin²A)
= √(1 − (8/17)²)
= √(1 − 64/289)
= √(225/289)
= 15/17
sin B = √(1 − cos²B)
= √(1 − (15/17)²)
= √(1 − 225/289)
= √(64/289)
= 8/17
sin A cos B + cos A sin B= (8/17 × 15/17) + (15/17 × 8/17)
= 120/289 + 120/289
= 240/289