sin

^{2}θ + cos

^{2}θ = 1

sin(

*A*+

*B*) = sin

*A*cos

*B*+ cos

*A*sin

*B*

and

cos(

*A*+

*B*) = cos

*A*cos

*B*- sin

*A*sin

*B*

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 sin

^{2}θ + cos

^{2}θ = 1 formula, since the formula for the unit circle is

*x*

^{2}+

*y*

^{2}= 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?