Question
Find the value of tan(75°) using the identity for
tan(A+B).Solution
We know tan(75°) = tan(45° + 30°). Using the formula tan(A+B) = (tanA + tanB) / (1 - tanA * tanB), tan(75°) = (tan(45°) + tan(30°)) / (1 - tan(45°) * tan(30°)). = (1 + 1/√3) / (1 - 1 * 1/√3) = (√3 + 1) / (√3 - 1). Multiplying numerator and denominator by (√3 + 1), = [(√3 + 1)²] / [(√3)² - (1)²] = (3 + 2√3 + 1) / (3 - 1) = (4 + 2√3) / 2 = 2 + √3.
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