sin(x+y)
 

 
圖,∠BEO 90,∠BAO 90,∠ACB 90,∠ADE 90

如果∠AOD x ∠BOA y則 ∠ABC x 直角三角形BOEsin(x+y)=$\frac{\overline{BE}}{\overline{OB}}$

sin(x+y)=$\frac{\overline{BE}}{\overline{OB}}$=$\frac{\overline{BC}+\overline{CE}}{\overline{OB}}$=$\frac{\overline{BC}+\overline{AD}}{\overline{OB}}$=$\frac{\overline{BC}}{\overline{OB}}$+$\frac{\overline{AD}}{\overline{OB}}$=$\frac{\overline{BC}}{\overline{OB}}$×$\frac{\overline{BA}}{\overline{BA}}$+$\frac{\overline{AD}}{\overline{OB}}$×$\frac{\overline{OA}}{\overline{OA}}$=$\frac{\overline{BC}}{\overline{BA}}$×$\frac{\overline{BA}}{\overline{OB}}$+$\frac{\overline{AD}}{\overline{OA}}$×$\frac{\overline{OA}}{\overline{OB}}$=

cos x sin y+sin x cos y=sin x cos y+cos x sin y

 



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