大学数学公式 大学数学介绍

1、三倍角公式：

sin3A = 3sinA-4(sinA)^3

cos3A = 4(cosA)^3 -3cosA

tan3a = tana tan(π/3 a)tan(π/3-a)

2、半角公式：

sin(A/2) = √{(1--cosA)/2}

cos(A/2) = √{(1 cosA)/2}

tan(A/2) = √{(1--cosA)/(1 cosA)}

cot(A/2) = √{(1 cosA)/(1-cosA)}

tan(A/2) = (1--cosA)/sinA=sinA/(1 cosA)

3、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

4、积化和差：

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)]

cos(a)sin(b) = 1/2*[sin(a b)-sin(a-b)]