If A + B = π/4, then (tan A + 1)(tan B + 1) is equal to:
2019
If A + B = π/4, then (tan A + 1)(tan B + 1) is equal to:
- A.
2
- B.
-1
- C.
1
- D.
√3
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Correct answer: A
Given A + B = π/4, evaluate (tan A + 1)(tan B + 1).
Step 1: Expand the product: (tan A + 1)(tan B + 1) = tan A·tan B + tan A + tan B + 1
Step 2: Use the tangent addition formula: tan(A + B) = (tan A + tan B) / (1 − tan A·tan B).
Step 3: Since A + B = π/4, tan(A + B) = 1, so tan A + tan B = 1 − tan A·tan B.
Step 4: Substitute into the expanded product: tan A·tan B + (1 − tan A·tan B) + 1 = 2
Therefore, the value of (tan A + 1)(tan B + 1) is 2.