已知sin(π/4+α)=1/3 求cos2α
问题描述：
已知sin(π/4+α)=1/3 求cos2α
答
sin(π/4+α)=sin^2 (π/4+α)=1/9
1-sin^2 (π/4+α)=cos^2 (π/4+α)=8/9
sin(π/4+α)=根号2/2 *(cosα+sinα)=1/3
cosα+sinα=根号2/6
cos(π/4+α)=cos π/4 * cosα-sin π/4 * sinα
=根号2/2 *(cosα-sinα) =2根号2/3
cosα-sinα=8/6
cos2α=cos^2 α -sin^2 α=(cosα+sinα)(cos-sinα)
=根号2/6 - 8/6 =根号2 - 8 / 6
自己做的.应该没大问题吧?