Trigonometry Help (1 Viewer)

[pasq]

I have a difficult questions I would like help with:

1. AP, PQ and QR are three equal intervals inclined at angles
α, 2α and 3α respectively to interval AB. Show that:
tan BAR =
sin α + sin2α + sin3α / cos α + cos2α + cos3α

 

[Paradoxica]

I have a difficult questions I would like help with:

1. AP, PQ and QR are three equal intervals inclined at angles
α, 2α and 3α respectively to interval AB. Show that:
tan BAR =
sin α + sin2α + sin3α / cos α + cos2α + cos3α

View attachment 33133

Let the length of each segment be l

Without Loss Of Generality, assume A is the origin.

The co-ordinates of P are lcosα, lsinα

The co-ordinates of Q are offset from P by (lcos2α, lsin2α)

So we have Q(lcosα + lcos2α, lsinα + lsin2α)

Similarly, the co-ordinates of R are offset from the co-ordinates of Q by (lcos3α, lsin3α)

So R(l(cosα + cos2α + cos3α), l(sinα + sin2α + sin3α))

And so, tan(BAR) follows as the quotient of ordinates.