已知sin(x+π÷6)=1/4,则sin(5π/6-x)+cos^2(π/3-x)=

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已知sin(x+π÷6)=1/4,则sin(5π/6-x)+cos^2(π/3-x)=

已知sin(x+π÷6)=1/4,则sin(5π/6-x)+cos^2(π/3-x)=
已知sin(x+π÷6)=1/4,则sin(5π/6-x)+cos^2(π/3-x)=

已知sin(x+π÷6)=1/4,则sin(5π/6-x)+cos^2(π/3-x)=
∵sin(x+π/6)=1/4
∴sin(5π/6-x)+cos²(π/3-x)=sin[π-(π/6+x)]+cos²[π/2-(x+π/6)]
=sin(π/6+x)+sin²(π/6+x) (应用诱导公式)
=1/4+(1/4)²
=5/16.

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