求值:tan6度*tan42度*tan66度*tan78度

解:方法1: tan6tan42tan66tan78 =(tan6tan54tan66tan42tan78)/tan54 =[tan6tan(60-6)tan(60+6)tan42tan78]/tan54 =(tan18tan42tan78)/tan54 =tan54/tan54 =1.

注: (1)以上省略了"度"; (2)这里用了正切3倍角公式: tanxtan(60-x)tan(60+x) =tan3x.

方法2:原式=tan6*cot48*cot24*cot12 =1

具体方法: 原式= sin6cos12cos24cos48

                            -------------------        =

                           cos6sin12sin24sin48

                          (sin30-sin18)(cos60+cos36)

                          _ ------------------------          =

                           (sin30+sin18)(cos60-cos36)

                             (0.5-sin18)(0.5+cos36)

                            _------------------------        =

                             (0.5+sin18)(0.5-cos36)

                            (0.25-sin18cos36)+0.5(cos36-sin18)

                            _-----------------------------------            =

                            (0.25-sin18cos36)-0.5(cos36-sin18)

                            1 要用到积化和差公式。