已知cos(a+派\4)=3\5,[派\2,3派\2],求cos(2a+派\4)的值

已知cos(a+派\4)=3\5,[派\2,3派\2],求cos(2a+派\4)的值
已知cos(a+派\4)=3\5,[派\2,3派\2],求cos(2a+派\4)的值

已知cos(a+派\4)=3\5,[派\2,3派\2],求cos(2a+派\4)的值
cos(a+π/4)=3/5
cos(2a+π/2)=2cos^2(a+π/4)-1=-7/25
∵a∈[π/2,3π/2],∴结合上式2a∈[π,3π/2],
又sin2a=-cos(2a+π/2)=7/25
cos2a=-24/25
cos(2a+π/4)=cos2a*cos(π/4)-sin2a*sin(π/4)
=-17√2/50