解析:
根据正弦定理:(AB/BC)×(BC/CD)×(CD/AD)×(AD/AB)=1 ☆★☆ (sin(270/7)/sin(480/7))×(sin(390/7)/sin(270/7))×(sin((540/7)-x)/sin(330/7))×(sin(240/7)/sinx)=1,
(sin((540/7)-x)/sinx)=(sin(480/7)sin(330/7)/sin(240/7)sin(390/7))=(2sin(240/7)cos(240/7)sin(330/7)/sin(240/7)sin(390/7))=(cos(240/7)sin(330/7)/sin30sin(390/7))
=(sin(90-(240/7))sin(330/7)/sin30sin(390/7))=(sin(390/7)sin(330/7)/sin30sin(390/7))=(sin(330/7)/sin30)=(sin((540/7)-30)/sin30),x=30。
注意:用到2倍角公式:sin(480/7)=2sin(240/7)cos(240/7),用到诱导公式:sin(90-(240/7))=cos(240/7)。
根据正弦定理:(AB/BC)×(BC/CD)×(CD/AD)×(AD/AB)=1 ☆★☆ (sin(270/7)/sin(480/7))×(sin(390/7)/sin(270/7))×(sin((540/7)-x)/sin(330/7))×(sin(240/7)/sinx)=1,
(sin((540/7)-x)/sinx)=(sin(480/7)sin(330/7)/sin(240/7)sin(390/7))=(2sin(240/7)cos(240/7)sin(330/7)/sin(240/7)sin(390/7))=(cos(240/7)sin(330/7)/sin30sin(390/7))
=(sin(90-(240/7))sin(330/7)/sin30sin(390/7))=(sin(390/7)sin(330/7)/sin30sin(390/7))=(sin(330/7)/sin30)=(sin((540/7)-30)/sin30),x=30。
注意:用到2倍角公式:sin(480/7)=2sin(240/7)cos(240/7),用到诱导公式:sin(90-(240/7))=cos(240/7)。