Bob

One final thought: The compound angle formulas work whatever the angles used. They aren't limited to acute angles. The proof above only works for acute angles; in fact, the diagram breaks down if A + B is over 90. I think that is why I prefer other proofs that are more general. The rotational matrix proof is my favourite.

]]>If you put alpha = beta = A, you get the double angle formulas.

eg.

Now put theta = 2A and you can re-arrange to get

and so on.

Is that what you wanted?

Bob

]]>Well done!

Bob

]]>Bob

]]>I did wonder if that's what you wanted. I could remember the formulas I gave easily so I took the line of least effort.

There are many ways of proving the compound angle formulas. The trig. approach is the first I met whilst still at school, but I haven't used it since. So I've had to dig deep in my memory.

So, make a triangle ABC with angle A = alpha and angle B = 90

Make a perpendicular line CD so that angle DCA = 90.

Choose the position of D so that DAC = beta.

Draw DF perpendicular to AB with F on AB, and finally CE perpendicular to DF with E on DF.

Call the point where DF and AC cross point G.

AGF = CGD = 90 minus alpha so GDC = alpha.

note EF = CB

The cosine formula is very similar. I'll leave it as an exercise.

hint AF = AB - FB

Bob

]]>I already did in the other thread. It looks like it is a tough nut to crack.

]]>I'll post a note to MIF.

Bob

]]>It's working for me, but only on its own!]]>

I've edited them to dotplus for now.

Bob

]]>Why is "plus" written everywhere "+" should go.

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