Question

Given that `tan (θ_1 + θ_2) = (tan θ_1 + tan θ_2)/(1 - tan θ_1 tan θ_2)` Find (θ₁ + θ₂) when tan θ₁ = `1/2 and tan θ_2 = 1/3`.

Answer 1

We have,
tan θ₁ = `1/2 and tan θ_2 = 1/3`

∴ `tan (θ_1 + θ_2) = (tan θ_1 + tan θ_2)/(1 - tan θ_1 tan θ_2)`

= `(1/2 + 1/3)/(1 - 1/2 xx 1/3)`

= `(5/6)/(1 - 1/6)`

= `tan (θ_1 + θ_2) = (5/6)/(5/6)`

= tan (θ₁ + θ₂) = 1

= θ₁ + θ₂ = 45°