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General Solution of Trigonometric Equation

Prove that if...

Question

Prove that if $α + β = π / 4$ , then (1 + tan $α$ ) (1 + tan $β$ ) = 2

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Solution

$tan (α + β) = tan \frac{π}{4}$

$⟹ \frac{tan α + tan β}{1 - tan α tan β} = 1$

$⟹ tan α + tan β + tan α tan β = 1$

$⟹ 1 + tan α + tan β + tan α tan β = 2$

$⟹ (1 + tan α) (1 + tan β) = 2$

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General Solution of Trigonometric Equation

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