SOLUTION: How do I express sin(x+y+z) in terms of cosines and sines of x, y and z? I know that you can express sin(x+y) into =sinxcosy+cosxsiny

Question 920256: How do I express sin(x+y+z) in terms of cosines and sines of x, y and z?
I know that you can express
sin(x+y) into
=sinxcosy+cosxsiny

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Let . You don't have to use Q. Just any other variable not being used.

will then turn into after you replace "x+y" with "Q" (the substitution is valid based on the definition we made above).

Expand out :

Now we have . Next, replace every Q with "x+y" to get

replace every Q with "x+y"

The next step is to expand and

which you will use to replace and in

Replace with

Replace with

Distribute

---------------------------------------------------------------------------------------------

So expands out into

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim
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