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If x + y = 45deg, which of the following identities holds?

1. (1 + tan(x))(1 + tan(y)) = 2
2. (1 + tan(x))(1 + tan(y)) = 1
3. (1 + tan(x))(1 + tan(y)) = 1/2
4. (1 + tan(x))(1 + tan(y)) = sqrt(2)

Correct answer: (1 + tan(x))(1 + tan(y)) = 2

Solution

Since x + y = 45deg gives tan(x) + tan(y) + tan(x)*tan(y) = 1, expanding the product yields 2.

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