Question

cos40*cos20*cos100 - вычислить.

Answer 1

Ответ:

$-\dfrac{1}{8}$

Пошаговое объяснение:

$\cos40^\circ \cos20^\circ\cos100^\circ=\left[\sin 20^\circ\neq 0\right]=\dfrac{ 2\sin20^\circ\cos20^\circ \cdot \cos40^\circ\cos100^\circ}{2\sin20^\circ}=\\ =\left[\sin2\alpha=2\sin\alpha\cos\alpha\right]=\dfrac{ \sin40^\circ\cdot \cos40^\circ\cos100^\circ}{2\sin20^\circ}=\dfrac{ 2\sin40^\circ\cos40^\circ\cdot \cos100^\circ}{4\sin20^\circ}=\\ =\dfrac{ \sin80^\circ\cdot \cos100^\circ}{4\sin20^\circ}=[\sin(90^\circ-\alpha)=\cos\alpha;\cos(90^\circ+\alpha)=-\sin\alpha]=$

$=\dfrac{ \cos10^\circ\cdot (- \sin10^\circ)}{4\sin20^\circ}=-\dfrac{ 2\sin10^\circ\cos10^\circ}{8\sin20^\circ}=-\dfrac{ \sin20^\circ}{8\sin20^\circ}=-\dfrac{1}{8}$