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Let alpha and beta be positive acute angles with cos(alpha) = 3/5 and cos(beta) = 4/5. Find the value of cos((alpha - beta)/2).

1. 7/(5*sqrt(2))
2. 9/(5*sqrt(2))
3. 1/sqrt(2)
4. 9/10

Correct answer: 7/(5*sqrt(2))

Solution

Compute sin alpha and sin beta, then cos(alpha-beta), then take the half-angle.

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