If cos A = 5/13 and sin B = 12/13 find sin A cos B + cos A sin B:
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Correct answer: A
Explanation
Has been given :
cos A = 5/13
sin B = 12/13
According to the formula:
sin(A + B) = sin A cos B + cos A sin B
sin²θ + cos²θ = 1
sin A = √(1 − cos²A)
= √(1 − (5/13)²)
= √(1 − 25/169)
= √(144/169)
= 12/13
cos B = √(1 − sin²B)
= √(1 − (12/13)²)
= √(1 − 144/169)
= √(25/169)
= 5/13
Now
sin A cos B + cos A sin B
= (12/13 × 5/13) + (5/13 × 12/13)
= 60/169 + 60/169
= 120/169