四倍角公式：
sin4A=-4×(cosA×sinA×(2×sinA^2-1))
cos4A=1+(-8×cosA^2+8×cosA^4)
tan4A=(4×tanA-4×tanA^3)/(1-6×tanA^2+tanA^4)
扩展资料
1、两角和与差的三角函数
sin(a+b)=sin(a)cos(b)+cos(α)sin(b)
cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
sin(a-b)=sin(a)cos(b)-cos(a)sin(b)
cos(a-b)=cos(a)cos(b)+sin(a)sin(b)
tan(a+b)=(tan(a)+tan(b))/(1-tan(a)tan(b))
tan(a-b)=(tan(a)-tan(b))/(1+tan(a)tan(b))
2、三角函数和差化积公式
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)
3、积化和差公式
sin(a)sin(b)=-1/2*[cos(a+b)-cos(a-b)]
cos(a)cos(b)=1/2*[cos(a+b)+cos(a-b)]
sin(a)cos(b)=1/2*[sin(a+b)+sin(a-b)]
4、二倍角公式
sin(2a)=2sin(a)cos(a)
cos(2a)=cos^2(a)-sin^2(a)=2cos^2(a)-1=1-2sin^2(a)
5、半角公式
sin^2(a/2)=(1-cos(a))/2
cos^2(场/2)=(1+cos(a))/2
tan(a/2)=(1-cos(a))/sin(a)=sin(a)/(1+cos(a))
6、万能公式
sin(a)= (2tan(a/2))/(1+tan^2(a/2))
cos(a)= (1-tan^2(a/2))/(1+tan^2(a/2))
tan(a)= (2tan(a/2))/(1-tan^2(a/2))
