Proof of the Addition Identies

  • Thread starter Bogrune
  • Start date
So throughout this entire semester in my Precalculus class my instructor told us that for solving trigonometric formulas, we will only learn about using these three formulas:
sin2θ + cos2θ = 1
sin(A+B) = sinAcosB + cosAsinB

and

cos(A+B) = cosAcosB - sinAsinB

For about two months we've studied trigonometry using almost nothing but these three formulas, and I understood how to use them well. I understood proof of the sin2θ + cos2θ = 1 formula, since the formula for the unit circle is x2 + y2 = 1, but I've never understood the proof for the addition identities. Just out of curiosity, can anyone show me proof of both addition identities?
 
Huh... and to think that the last place that I was going to look for proof was Wikipedia since it always explains even the most simple math-related topic as if it was Complex Analysis. Thanks for the help though!
 

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