Вычислить (корень из 2) *(sin70+sin 20)) : (sin 80*cos15- cos 80*cos75).. Created by Rekonsiv. matematika-ru

Вычислить (корень из 2) *(sin70+sin 20)) : (sin 80*cos15- cos 80*cos75)...

Rekonsiv @Rekonsiv

July 2022 1 17 Report

Вычислить (корень из 2) *(sin70+sin 20)) : (sin 80*cos15- cos 80*cos75).

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$\frac{ \sqrt{2}sin70+sin20}{sin80cos15-cos80cos75}= \frac{ \sqrt{2}*sin (45+25)+sin(45-25)}{sin80cos(90-75)-cos80cos75}=\\\\ \frac{ \sqrt{2}sin45cos25+sin25cos45+sin45cos25-sin25cos45}{sin80cos75-cos80cos75}= \frac{\sqrt{2}*2sin45cos25}{cos(80+75)}=\\\\ \frac{2\sqrt{2}sin45cos25}{cos(180-25)}=\frac{2\sqrt{2}sin45cos25}{-cos25}= \\ \\ -2 \sqrt{2}* \frac{ \sqrt{2}}{2}=-\frac{-2\sqrt{2}*\sqrt{2}}{2}=- \frac{8}{2}=-4$

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