Question

已知α为锐角,那：根号下(sinα-1)²=1-sinα 要理由

Answer 1

1+cosa-sinb+sinasinb=0

1+cosa=sinb-sinasinb=sinb(1-sina).(1)

1-cosa-cosb+sinacosb=0

1-cosa=cosb-sinacosb=cosb(1-sina).(2)

(1)^2+(2)^2

(1-cosa)^2+(1+cosa)^2=(1-sina)^2

2+2cos^2a=1-2sina+sin^2a

4-2sin^2a=1-2sina+sin^2a

3sin^2a-2sina-3=0,

sina=(1+√10)/31,舍去

或sina=(1-√10)/3

故sina=(1-√10)/3