Need pre-calculus help on how to prove(verify) an equation

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tanθ+β =pi/4, show that (1+tanθ)(1+tan )=2

May 28th, 2015

Let 

tanֿ¹(1/2) = α 
tanֿ¹(1/3) = β 
α + β = θ 

tanθ 
= tan(α + β) 
= [tanα + tanβ] / [1 - tanαtanβ] 
= [(1/2) + (1/3)] / [1 - (1/2)(1/3)] 
= [3 + 2] / [6 - 1] 
= 1 

Angles α and β are both acute, so α + β < π, θ < π. This means θ must be in quadrant 1 or 2. 

tanθ = 1 
θ = π/4 
α + β = π/4 
tanֿ¹(1/2) + tanֿ¹(1/3) = π/4

so from above we know that 

tanθ = 1 
by putting 

(1+tanθ)(1+tan )

(1+1)(1+0)=2

May 28th, 2015

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