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Quadratic Formula

If tanα = 1...

Question

If $tan α = \frac{1}{2}, tan β = \frac{1}{3}$ , show that $α + β = π / 4$

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Solution

$tan α = \frac{1}{2}$
$tan β = \frac{1}{3}$
$tan (α + β) = \frac{tan α + tan β}{1 - tan α tan β}$
$= \frac{\frac{1}{2} + \frac{1}{3}}{1 - \frac{1}{6}}$
$tan (α + β) = \frac{\frac{5}{6}}{\frac{5}{6}} = 1$
$∴ α + β = \frac{π}{4}$

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