Sin (73 П/24) * sin (37 П/24) * sin (37 П/12). Вычислить.

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Алгебра

Толяха

6 августа, 10:45

Sin (73 П/24) * sin (37 П/24) * sin (37 П/12). Вычислить.

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Камилла · Answer 1

Sin (73π/24) * sin (37π/24) * sin (37π/12) = sin (3π+π/24) sin (π+13π/24) sin (3π+π/12) =

-sinπ/24 * (-sin13π/24) * (-sinπ/12) = - 1/2 (cos (13π/24-π/24) - cos (13π/24+π/24)) *

*sinπ/12=-1/2 (cosπ/2-cos7π/12) * sinπ/12=1/2cos7π/12*sinπ/12=

=1/4 (sin (π/12-7π/12) + sin (π/12+7π/12)) = 1/4 (sin (-π/2) + sin2π/3) =

=1/4 * (-1) + 1/4*√3/2=-1/4+√3/8