Thank you arildno I understand that now. It took a while but I got there in the end.

Going the path along with the half angle product formula would have given you precisely the same expression.
With a lot less work!

ehild
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arildno
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Thank you arildno I understand that now. It took a while but I got there in the end.

However, I would like to say that ehild's scheme, although apparently clunky, is a VERY important technique in many other fields as well, i.e, understanding and using the concept of linearly independent functions in order to solve particular problems.

It is, in a manner of speaking, a generally more powerful tool than trig identity tables that you'll gradually learn to appreciate.

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