已知sin(X-π/4)=√2/4,则tanx+(1/tanx)的值

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已知sin(X-π/4)=√2/4,则tanx+(1/tanx)的值

已知sin(X-π/4)=√2/4,则tanx+(1/tanx)的值
已知sin(X-π/4)=√2/4,则tanx+(1/tanx)的值

已知sin(X-π/4)=√2/4,则tanx+(1/tanx)的值
∵ sin(X-π/4)=√2/4
∴ sinx*sin(π/4)-cosx*cos(π/4)=√2/4
∴ sinx*(√2/2)-cosx*(√2/2)=√2/4
∴ sinx-cosx=1/2
∴ (sinx-cosx)²=1/4
∴ sin²x+cos²x-2sinxcosx=1/4
∴ 1-2sinxcosx=1/4
∴ sinxcosx=3/8
tanx+(1/tanx)
=sinx/cosx+cosx/sinx
=sin²x/(sinxcosx)+cos²x/(sinxcosx)
=(sin²x+cos²x)/(sinxcosx)
=1/(sinxcosx)
=1/(3/8)
=8/3

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