Question

已知cos（α+π/4）=3/5，π/2≤α＜3π/2，求cos（2α+π/4）

Answer 1

π/2≤a≤3π/2
cos(a+π/4)=3/5>0
a+π/4>3π/2
3π/2<a+π/4≤7π/4
sin(a+π/4)=-√[1-cos²(a+π/4)]=-4/5
sina=[sin(a+π/4)-π/4]=√2/2*[sin(a+π/4)-cos(a+π/4)]=√2/2*(-4/5-3/5)=-7√2/10
cosa=-√(1-sin²a)=-√2/10
cos2a=2cos²a-1=-24/25,sin2a=2sinacosa=7/25
cos(2a+π/4)=√2/2(cos2a-sin2a)=-31√2/50

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