Question

Use a Double- or Half-Angle Formula to solve the equation in the interval. Help please!
tan θ/2 − sin θ = 0

Answer 1

well if you use half angle then its basically

\[\tan(\frac{\theta}{2}) = t\]

and

\[\sin(\theta) = \frac{2t}{1 + t^2}\]

it comes from the trig identity



and the fact that

\[\sin(\theta) = 2\sin(\frac{\theta}{2})\cos(\frac{\theta}{2})\]

so making the subsitutions you get

\[t - \frac{2t}{\sqrt{1 + t^2}} = 0\]

so you just need to solve for t.

hope it helps