题目

求证1÷sin12°=1÷sin24° 1÷sin48° 1÷sin84°
求证:1÷sin12°=1÷sin24°+ 1÷sin48°+ 1÷sin84°

提问时间：2021-01-01

答案

sin48=sin132=sin(84+48)=sin(84-48)+2sin48cos84
=sin36+2sin48cos84==sin(12+24)+2sin48cos84
=sin(24-12)+2sin12cos24+2sin48cos84
=sin12+2sin12cos24+2sin48sin6
所以
sin48=sin12+2sin12cos24+2sin48sin6
1=sin12/sin48+2sin12cos24/sin48+2sin6
=sin12/sin48+sin12/sin24+2sin6
1/sin12=1/sin48+1/sin24+2sin6/sin12
所以
1/sin12=1/sin24 + 1/sin48 + 1/cos6
所以
1/sin12=1/sin24 + 1/sin48 + 1/sin84