原文地址:高中118个三角函数公式作者:王学刚_培训专家三角函数公式 两角和公式 sin(a+b) = sinacosb+cosasinb sin(a-b) = sinacosb-cosasinb cos(a+b) = cosacosb-sinasinb cos(a-b) = cosacosb+sinasinb tan(a+b) = (tana+tanb)(1-tanatanb) tan(a-b) = (tana-tanb)(1+tanatanb) cot(a+b) = (cotacotb-1)(cotb+cota) cot(a-b) = (cotacotb+1)(cotb-cota) 倍角公式 tan2a = 2tana(1-tan^2 a) sin2a=2sina?cosa cos2a = cos^2 a--sin^2 a =2cos^2 a-1 =1-2sin^2 a 三倍角公式 sin3a = 3sina-4(sina)^3; cos3a = 4(cosa)^3 -3cosa tan3a = tan a ? tan(π3+a)? tan(π3-a) 半角公式 sin(a2) = √{(1--cosa)2} cos(a2) = √{(1+cosa)2} tan(a2) = √{(1--cosa)(1+cosa)} cot(a2) = √{(1+cosa)(1-cosa)} tan(a2) = (1--cosa)sina=sina(1+cosa) 和差化积 sin(a)+sin(b) = 2sin[(a+b)2]cos[(a-b)2] sin(a)-sin(b) = 2cos[(a+b)2]sin[(a-b)2] cos(a)+cos(b) = 2cos[(a+b)2]cos[(a-b)2] cos(a)-cos(b) = -2sin[(a+b)2]sin[(a-b)2] tana+tanb=sin(a+b)cosacosb 积化和差 sin(a)sin(b) = -12*[cos(a+b)-cos(a-b)] cos(a)cos(b) = 12*[cos(a+b)+cos(a-b)] sin(a)cos(b) = 12*[sin(a+b)+sin(a-b)] cos(a)sin(b) = 12*[sin(a+b)-sin(a-b)] 诱导公式 sin(-a) = -sin(a) cos(-a) = cos(a) sin(π2-a) = cos(a) cos(π2-a) = sin(a) sin(π2+a) = cos(a) cos(π2+a) = -sin(a) sin(π-a) = sin(a) cos(π-a) = -cos(a) sin(π+a) = -sin(a) cos(π+a) = -cos(a) tga=tana = sinacosa 万能公式 sin(a) = [2tan(a2)]  {1+[tan(a2)]^2} cos(a) = {1-[tan(a2)]^2}  {1+[tan(a2)]^2} tan(a) = [2tan(a2)]{1-[tan(a2)]^2} 其它公式 a?sin(a)+b?cos(a) = [√(a^2+b^2)]*sin(a+c) [其中,tan(c)=ba] a?sin(a)-b?cos(a) = [√(a^2+b^2)]*cos(a-c) [其中,tan(c)=ab] 1+sin(a) = [sin(a2)+cos(a2)]^2; 1-sin(a) = [sin(a2)-cos(a2)]^2;;