Deriving a trig thing

  • #1
Can anyone tell me how to derive the sin(x+y) and cos(x+y) expansions? The ones that are like cos x sin y or sin y cos x + other stuff?
Preferrably, could this be derived with Euler's formula alone? Or something not too geometric? (All those OAs and OBs and XBs and XYs on geometric diagrams confuse me too much to follow)
Thank you.
 

Answers and Replies

  • #2
mathman
Science Advisor
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You could use Euler's formula. It is tedious, but straightforward.
 
  • #3
StatusX
Homework Helper
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Another way is to use the 2X2 rotation matrices R([itex]\theta[/itex]), which have R(x)R(y)=R(x+y). This is equivalent to using Euler's formula, only you're working in R^2 instead of the complex numbers.
 
  • #4
VietDao29
Homework Helper
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There's a short proof at wikipedia, you can view it at the end of this page.
It is, however, not a completed proof, but you can get some ideas about proving it. :)
 

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