{sin^2 80°/4(cos40°--cos^3 40°) }(1+根号3tan10°)

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{sin^2 80°/4(cos40°--cos^3 40°) }(1+根号3tan10°)

{sin^2 80°/4(cos40°--cos^3 40°) }(1+根号3tan10°)
{sin^2 80°/4(cos40°--cos^3 40°) }(1+根号3tan10°)

{sin^2 80°/4(cos40°--cos^3 40°) }(1+根号3tan10°)
{sin^2 80°/4(cos40°--cos^3 40°) }(1+根号3tan10°)
={sin^2 80°/[4cos40°(1-cos^2 40°) }(1+根号3tan10°)
={sin^2 80°/[4cos40°sin^2 40°) }(1+根号3tan10°)
={sin^2 80°/[2sin40°cos40°*2sin40°) }(1+根号3tan10°)
={sin^2 80°/[sin80°sin40°) }(1+根号3tan10°)
={sin 80°/sin40° }(1+根号3tan10°)
={cos 10°/sin40° }(1+根号3tan10°)
=(cos 10°+根号3sin10°)/sin40°
=2(cos60°cos10°+sin60°sin10°)/sin40°
=2cos(60°-10°)/sin40°
=2cos50°/sin40°
=2sin40°/sin40°
=2