已知sinα+cosα =√2/2,求1/(sin2α)+1/(cos2α)的值

问题描述:

已知sinα+cosα =√2/2,求1/(sin2α)+1/(cos2α)的值

sinα+cosα =√2/2,
两边平方,
1+sin2α=1/2,
sin2α=-1/2,
cos2α=±√3/2,
1/(sin2α)+1/(cos2α)=-2±2√3/3.