Question

Find the measure of angle θ in the following when θ is acute.

3 tan² θ = 1

show that `(2 tan θ)/(1− tan^2 θ )= tan 2θ`

Answer 1

Given:

`3 tan^2 θ = 1 → tan^2 θ = 1/3`

tan θ = ± `1/sqrt3`

Since θ is acute (0° < θ < 90°), tan θ > 0.

tan θ = `1/sqrt3`

θ = 30°

Use the addition formula:

tan (α + β) = `(tan α + tan β)/(1 − tan α tan β)`.   ...[Put α = β = θ]

`tan (2θ) = (tan θ + tan θ)/(1 − tan θ tan θ) = (2 tan θ)/(1 − tan^2 θ)`