已知sin(x+π/4)=-3/4,则sin2x的值为
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已知sin(x+π/4)=-3/4,则sin2x的值为已知sin(x+π/4)=-3/4,则sin2x的值为已知sin(x+π/4)=-3/4,则sin2x的值为解sin2x=-cos(2x+π/2)
已知sin(x+π/4)=-3/4,则sin2x的值为
已知sin(x+π/4)=-3/4,则sin2x的值为
已知sin(x+π/4)=-3/4,则sin2x的值为
解
sin2x
=-cos(2x+π/2)
=-cos[2(x+π/4)]
=-[1-2sin²(x+π/4)]
=2sin²(x+π/4)-1
=2*(3/4)²-1
=9/8-1
=1/8
sin(x+π/4)=-3/4
sinx+cosx=-3v2/4
1+sin2x=9/8
sin2x=1/8
sin(x+π/4)=sinxcosπ/4+cosxsinπ/4=根号2/2(sinx+cosx)=-3/4
上式两边平方
1/2*(1+2sinxcosx)=9/16
1+sin2x=9/8
sin2x=1/8
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