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If sin(alpha) = 15/17 and cos(beta) = 12/13 (both alpha, beta acute), evaluate sin(alpha + beta), cos(alpha - beta) and tan(alpha + beta).

1. sin(a+b) = 171/221, cos(a-b) = 220/221, tan(a+b) = 171/140
2. sin(a+b) = 220/221, cos(a-b) = 171/221, tan(a+b) = 220/21
3. sin(a+b) = 21/221, cos(a-b) = 140/221, tan(a+b) = 21/220
4. sin(a+b) = 140/221, cos(a-b) = 171/221, tan(a+b) = 220/171

Correct answer: sin(a+b) = 220/221, cos(a-b) = 171/221, tan(a+b) = 220/21

Solution

With cos(alpha) = 8/17 and sin(beta) = 5/13, the addition formulas yield sin(a+b) = 220/221, cos(a-b) = 171/221, tan(a+b) = 220/21.

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