已知函数f(x)=(1+cotx)sin^2(x)-2sin(x+∏/4)sin(x-∏/4),若tana=2,求f(a
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已知函数f(x)=(1+cotx)sin^2(x)-2sin(x+∏/4)sin(x-∏/4),若tana=2,求f(a)
f(x)=(1+cotx)sin^2(x)-2sin(x+∏/4)sin(x-∏/4)
=sin^2(x)+sinxcosx+cos2x
=1/2(1-cos2x)+sinxcosx+cos2x
=1/2(sin2x+cos2x)+1/2
sin2x=2tanx/(1+tanxtanx)
cos2x=(1-tanxtanx)/(1+tanxtanx)
当tana=2,则sin2a=4/5,cos2x=-3/5
所以f(a)=1/2*(4/5-3/5)+1/2=3/5
=sin^2(x)+sinxcosx+cos2x
=1/2(1-cos2x)+sinxcosx+cos2x
=1/2(sin2x+cos2x)+1/2
sin2x=2tanx/(1+tanxtanx)
cos2x=(1-tanxtanx)/(1+tanxtanx)
当tana=2,则sin2a=4/5,cos2x=-3/5
所以f(a)=1/2*(4/5-3/5)+1/2=3/5
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