已知sin(x-π/4)=-1/3,则sin2x的值等于
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已知sin(x-π/4)=-1/3,则sin2x的值等于
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前辈们
过程!!!
在线等待 请帮帮忙
......
前辈们
过程!!!
sin2x = sin(x + π/4 + x - π/4)
= sin(x+π/4)cos(x-π/4) + cos(x+π/4)sin(x-π/4)
= cos[π/2 - (x +π/4)] cos(x-π/4) + sin[π/2 - (x+π/4)] sin(x-π/4)
= cos(x-π/4)cos(x-π/4) + sin(π/4 -x)sin(x-π/4)
= 1 - sin(x-π/4)sin(x-π/4) - sin(x -π/4)sin(x-π/4)
= 1 - 2 * (-1/3)(-1/3)
= 1 - 2/9
= 7/9
= sin(x+π/4)cos(x-π/4) + cos(x+π/4)sin(x-π/4)
= cos[π/2 - (x +π/4)] cos(x-π/4) + sin[π/2 - (x+π/4)] sin(x-π/4)
= cos(x-π/4)cos(x-π/4) + sin(π/4 -x)sin(x-π/4)
= 1 - sin(x-π/4)sin(x-π/4) - sin(x -π/4)sin(x-π/4)
= 1 - 2 * (-1/3)(-1/3)
= 1 - 2/9
= 7/9
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