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If alpha + beta = 90 deg, find the maximum value of sin(alpha) * sin(beta).

1. 1/2
2. 1
3. 1/4
4. sqrt(2)/2

Correct answer: 1/2

Solution

Substituting beta = 90 - alpha turns the product into (1/2) sin(2 alpha), which is largest (= 1/2) when 2 alpha = 90 deg, i.e. alpha = beta = 45 deg.

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