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Angle Sum Identity and Consistency

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Let cos⁡(α+β)=12\cos(\alpha + \beta) = \frac{1}{2}, cos⁡α=35\cos \alpha = \frac{3}{5}, and sin⁡β=45\sin \beta = \frac{4}{5}. What is the value of sin⁡αcos⁡β\sin \alpha \cos \beta?

A

1

B

0.5

C

0

D

No real value exists; the constraints are inconsistent.

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