Question

sin(A+B)=sinAcosB+cosAsinB

如何证明

Answer 1

如图所示作单位圆,设∠AOC=α,∠COD=β,则∠AOD=α+β,AO=1作AB⊥Ox交Ox于B,作AC⊥OC交OC于C,作CE⊥AB交AB于E,作CD⊥Ox交Ox于D易证△OBF∽△ACF∴∠COD=∠CAF=βsin (α+β)=sin∠AOD=AB/AO=AB=AE+EB=AE+CD=AC*cosβ+OC*sinβ=AO*sinαcosβ+AC*cosαsinβ=sinαcosβ+cosαsinβ