（√3tan48°-1）/(2sec48°)-cos36°得数是-1/2

Question

（√3tan48°-1）/(2sec48°)-cos36°
得数是-1 /2

Answer 1

（√3tan48°-1）/(2sec48°)-cos36°
=（√3sin48°-cos48）/2-cos36°
=(cos30sin48-sin30cos48)-cos36
=sin(48-30)-cos36
=sin18-cos36
=(sin18-cos36)*cos18/cos18
=(sin18*cos18-cos36*cos18)/cos18
(括号内的两项积化和差)
=[0.5sin36-0.5(cos54+cos18)]/cos18
=(0.5sin36-0.5cos54-0.5cos18]/cos18
(因为0.5sin36=0.5cos54)
=-0.5cos18/cos18
=-0.5
=-1/2