DIRECTION of R= tan θ = Q sinα/ P+ Qcosα. When P=Q?
tan θ = Q sinα/ P+ Qcosα
If P=Q, Prove θ= α/2
tan θ = P sinα/ P+ Pcosα
tan θ = P sinα/ P (1+ cosα)
tan θ = sinα/ 1+ cosα
the next steps please?
Update:K, I got it.
sin2α=2sinαcosα
sinα= 2sin(α/2)cos(α/2)
Substitute it there...
Thanks a lot!
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Tan θ = sinα / 1+cosα
We know that : cos 2α = 2cos^2 α – 1 ⇔ cos 2α + 1 = 2cos^2 α
Analog with : cosα + 1 = 2cos^2 (α/2)
sinα / 1+cosα = sinα / 2cos^2 (α/2)
= 2sin(α/2)cos(α/2) / 2cos^2 (α/2)
= sin(α/2) / cos(α/2)
= tan(α/2)
So, we get θ=α/2