Question

Aflați cu cât este egală următoarea expresie (din poză).

Answer 1

$E=16(cos^2 10 \textdegree+cos^2 50 \textdegree-sin 40 \textdegree sin 80 \textdegree)= \\ \\ =16(sin^280 \textdegree +sin^2 40 \textdegree-sin40 \textdegree sin80 \textdegree)= \\ \\ =16 \Big((sin80 \textdegree - sin 40 \textdegree)^2-sin 40\textdegree sin80 \textdegree \Big) \\ --------------------\\ \\ sin 80 \textdegree -sin 40\textdegree=2sin20 \textdegree cos60 \textdegree=sin 20\textdegree$

$sin40\textdegree sin 80 \textdegree= \frac{1}{2} (cos 40 \textdegree - cos 120\textdegree)= \frac{1}{2} cos40 \textdegree + \frac{1}{4}. \\ \\ E=16sin^2 20 \textdegree +8 cos^2 40 \textdegree +4= \\ \\ ~~~=16sin^2 20 \textdegree + 8(cos^2 20 \textdegree - sin^2 20 \textdegree ) +4 = \\ \\ ~~~=8sin^2 20 \textdegree +8cos^2 20 \textdegree +4= \\ \\ ~~~=8(sin^2 20 \textdegree + cos^2 20\textdegree )+4= \\ \\ ~~~=8 \cdot 1+4= \\ \\ ~~~=12.$