cos(x+TT/4)=3/5 TT/2<x<3TT/2,求cos(2x+TT/4)=?

来源：百度知道 编辑：UC知道 时间：2024/06/23 12:24:06
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x+π/4∈(3π/4,7π/4)
cos(x+π/4)=3/5>0
sin(x+π/4)=-4/5
3π/2<x+π/4<7π/4
5π/4<x<3π/2
2x+π/4∈(11π/4,13π/4)在2，3象限
cos(2x+π/4)<0
cos(2x+π/4)
=cos(2(x+π/4)-π/4)
=cos(2(x+π/4))cos(π/4)+sin(2(x+π/4))sin(π/4)
=(2(cos(x+π/4))^2-1)*√2/2+2sin(x+π/4)cos(x+π/4)*√2/2
=(2*9/25-1)*√2/2+2*(-4/5*3/5)√2/2
=-7/25*√2/2-24/25*√2/2
=√2/2*(-31/25)
=-(31√2)/50

cosx*cos(TT/4)-sinx*sin(TT/4)=3/5;
cosxsin(TT/4)+sinx*cos(TT/4)=-4/5;
cosx=-2^(1/2)/10;
sinx=-7*2(1/2)/10;
cos(2x+TT/4)=cosxcos(x+TT/4)-sinxsin(x+TT/4)=-31*2^(1/2)/50