Question

Вычислите 12sin 104* cos104*
sin208

Answer 1

Ответ:

$12\, sin104^\circ \cdot cos104^\circ \cdot sin208^\circ =6\, sin208^\circ \cdot sin208^\circ =6\, sin^2208^\circ=\\\\=6\, sin^2(180^\circ +28^\circ )=6\, sin^228^\circ \approx 6\cdot 0,469^2=1,32$

$P.S.\ \ 12\, sin104^\circ \cdot cos104^\circ \cdot cos208^\circ =6\, sin208^\circ \cdot cos208^\circ =3\, sin416^\circ =\\\\=3\, sin(360^\circ +56^\circ )=3\, sin56^\circ\approx 3\cdot 0,829=2,487$

$\star \ \ 2\, sina\cdot cosa=sin2a\ \ \star$

Answer 2

$12sin104^0cos104^0sin208^0=\\\\=6(2sin104^0cos104^0)sin208^0=\\\\=6sin(2*104^0)sin208^0=\\\\=6sin208^0sin208^0=\\\\=6sin^2208^0$