Question

Use trigonometric identities to solve tan(2θ)+tan(θ)=0 exactly for 0≤θ≤π.

Answer 1

`tan (2 \theta)+tan \theta = (2 tan \theta)/(1-tan^2 \theta) +tan \theta = 0`
Multiplying equation by denominator gives:

`2 tan \theta + tan \theta (1-tan^2 \theta) = 0`
Factor out a tan

`tan \theta (3-tan^2 \theta) = 0 \\ tan\theta = 0, \pm √(3)`

`\theta = 0, (\pi)/(3), (2\pi)/(3)`