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)

擴充套件資料

1、兩角和與差的三角函式

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、三角函式和差化積公式

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、積化和差公式

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、半形公式

sin^2(a/2)=(1-cos(a))/2

cos^2(場/2)=(1+cos(a))/2

tan(a/2)=(1-cos(a))/sin(a)=sin(a)/(1+cos(a))

6、萬能公式

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))