和差化积，积化和差,三倍角公式

           SINx + SINy = 2SIN(x+y)/2 * COS(x-y)/2            SINx -SINy =2COS(x+y)/2 * SIN(x-y)/2           COSx+COSy=2COS(x+y)/2 * COS(x-y)/2           COSx-COSy=_2SIN(x+y)/2 * SIN(x-y)/2          记忆方法：把函数与角分别记忆。                          一。函数：  设：      S表示正弦，C表示余弦                                         S+S =2S * C        S-S = 2C * S                  想一想：S*C=?,      C*S=?                              C+C =2C *C       C-C =_2S * S                                 C*C=?,      S*S=?                          二。角的变化                               和 差 化 积，和 差 半；                              积 化 和 差，角 和 差。             举例：1.  化简：    cos80⁰+cos20 ⁰= 2cos(   ) * cos (    )                                  ( 80+20)/2=50  ,(80-20)/2=30                               cos80⁰+cos20⁰ =2cos50⁰ *cos30⁰                                                      =.............                         2.   求证：4COSx * COS(60 ⁰- x)*COS(60⁰ + x) =COS3x                                         4cosx*cos(60⁰ - x)*cos(60⁰ + x)                                                               =    4cosx * 0.5* ( cos120⁰ +cos2x)                                     = 2cosx (-cos60 ⁰ + cos2x )                                                                =  2cosx ( -0.5+cos2x )                                 = - cosx+2cosx*cos2x                                 = -cosx+2cosx * (2cosx*cosx-1)                                                                 = - cosx+4 (cosx ) ³ -2cosx                                      =4(cosx)³-3cosx                                 =cos3x                                引伸：cos3x =4(cosx)³ -3cosx..............4-3-3-1                                                        sin3x  =3 s i n x -4(sinx）^{.3...........}3-1-4-3                            tan3x =( 3tanx - (tanx) ³ )  / ( 1 -  3(tanx ）^2. ).....1-3-3-1                   又      tan2x =2tanx  /  ( 1 - ( tanx) ² )^{...................................}1-2-1                             tan4x =...........................................................1-4-6-4-1                             tan5x =.........................................................1-5-10-10-5-1                                  .........................................                                                                             1                                                                         1      1                                                                     1      2      1                                                                1       3     3        1                                                            1      4      6      4        1                                                        。    。     。   。      。     。                                    。。。。。。。。。。。。。。。。。。。。。