cos(a+兀/4)=3/5
根號(hào)2/2*cosa-根號(hào)2/2*sina=3/5
cosa-sina=3根號(hào)2/5
cosa=3根號(hào)2/5+sina
cosa^2+sina^2=1
(3根號(hào)2/5+sina)^2+sina^2=1
18/25+2sina^2+6根號(hào)2sina/5=1
2sina^2=7/25-6根號(hào)2sina/5
2sina^2+6根號(hào)2sina/5-7/25=0
sina=[-6根號(hào)2/5+根號(hào)(72/25+56/25)]/4=[-6根號(hào)2/5+8根號(hào)2/5]/4=根號(hào)2/10
或sina=[-6根號(hào)2/5-根號(hào)(72/25+56/25)]/4=[-6根號(hào)2/5-8根號(hào)2/5]/4=-7根號(hào)2/10
因?yàn)樨?2小于或等于a小于3兀/2
所以sina=-7根號(hào)2/10
cos（2a+兀/4)=根號(hào)2/2*cos2a-根號(hào)2/2*sin2a=根號(hào)2/2-根號(hào)2sina^2-根號(hào)2sinacosa
=根號(hào)2/2-根號(hào)2sina^2-根號(hào)2sina(3根號(hào)2/5+sina)
=根號(hào)2/2-根號(hào)2sina^2-6sina/5-根號(hào)2sina^2
=-2根號(hào)2sina^2-6sina/5+根號(hào)2/2
=-根號(hào)2(7/25-6根號(hào)2sina/5)-6sina/5+根號(hào)2/2
=12sina/5-7根號(hào)2/25-6sina/5+根號(hào)2/2
=6sina/5+11根號(hào)2/50
=6(-7根號(hào)2/10)/5+11根號(hào)2/50
=-42根號(hào)2/50+11根號(hào)2/50
=-31根號(hào)2/50