[latex]E=16(cos^2 10 extdegree+cos^2 50 extdegree-sin 40 extdegree sin 80 extdegree)= \ \ =16(sin^280 extdegree +sin^2 40 extdegree-sin40 extdegree sin80 extdegree)= \ \ =16 Big((sin80 extdegree - sin 40 extdegree)^2-sin 40 extdegree sin80 extdegree Big) \ --------------------\ \ sin 80 extdegree -sin 40 extdegree=2sin20 extdegree cos60 extdegree=sin 20 extdegree [/latex] [latex]sin40 extdegree sin 80 extdegree= frac{1}{2} (cos 40 extdegree - cos 120 extdegree)= frac{1}{2} cos40 extdegree + frac{1}{4}. \ \ E=16sin^2 20 extdegree +8 cos^2 40 extdegree +4= \ \ ~~~=16sin^2 20 extdegree + 8(cos^2 20 extdegree - sin^2 20 extdegree ) +4 = \ \ ~~~=8sin^2 20 extdegree +8cos^2 20 extdegree +4= \ \ ~~~=8(sin^2 20 extdegree + cos^2 20 extdegree )+4= \ \ ~~~=8 cdot 1+4= \ \ ~~~=12.[/latex]