【高一数学】紧急帮忙~好的加分~

π/2<=a<=3π/2
所以3π/4<=a+π/4<=7π/4
cos(a+π/4)>0
所以3π/2<a+π/4<=7π/4
所以5π/4<a<=3π/2
所以cosa<0,sina<0
sina+cosa<0

cos(a+π/4)=cosacosπ/4-sinasinπ/4=(√2/2)(cosa-sina)=3/5
cosa-sina=3√2/5
两边平方，且(sina)^2+(cosa)^2=1
所以1-2sinacosa=18/25
2sinacosa=7/25
(sina+cosa)^2=1+2sinacosa=32/25
sina+cosa=-4√2/5
所以sin2a=2sinacosa=7/25
cos2a=(cosa)^2-(sina)^2=(cosa+sina)(cosa-sina)=-24/25

cos(2a+π/4)=cos2acosπ/4-sin2asinπ/4=(√2/2)(cos2a-sin2a)
=(√2/2)*(-31/25)
=-31√2/50