Trigonometric EquationMedium
Question
If α + β = 
and β + γ = α, then tan α equals
and β + γ = α, then tan α equals Options
A.2(tan β + tan γ)
B.tan β + tan γ
C.tan β + 2 tan γ
D.2 tan β + tan γ
Solution
Given, α + β = π / 2
⇒ α = (π / 2) - β
⇒ tan α = tan (π / 2 - β)
⇒ tan α = cot β
⇒ tan α tan β = 1
Again β + γ = α
⇒ γ = (α - β)
⇒ an γ = tan(α - β)
⇒
⇒
∴ 2 tan γ = tan α - tan β
⇒ tan α = tan β + 2 tan γ
⇒ α = (π / 2) - β
⇒ tan α = tan (π / 2 - β)
⇒ tan α = cot β
⇒ tan α tan β = 1
Again β + γ = α
⇒ γ = (α - β)
⇒ an γ = tan(α - β)
⇒
⇒
∴ 2 tan γ = tan α - tan β
⇒ tan α = tan β + 2 tan γ
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