Упростить выражение cos^2a-cos(a+ pi/6)cos(a-pi/6). Created by iluha23. matematika-ru

6)...

Amaimoon

Verified answer

Cos²α-cos(α+π/6)*cos(α-π/6)
cos²α-1/2(cos(α+π/6+a-π/6) + cos(α+π/6-α+π/6))
cos²α-1/2(cos2α+cos π/3) ;
cos²α-1/2cos2α-1/2*1/2 ;
cos²α - cos2α/2 - 1/4 ; домножим все на 4/4.
(4cos²α-2cos2α - 1)/4 = (4cos²α - 2(2cos²α-1) - 1 ) /4;
(4cos²α-4cos²α+2-1)/4 = 1/4

2 votes Thanks 6

mukus13 ответ 1/4 - подредактируйте, пожалуйста

iluha23 Спасибо

mukus13

Verified answer

$cos^2 \alpha -cos( \alpha + \frac{ \pi }{6} )cos( \alpha - \frac{ \pi }{6} )=cos^2 \alpha - \frac{1}{2}[cos( \alpha + \frac{ \pi }{6} - \alpha +\frac{ \pi }{6} )+$ $+cos( \alpha + \frac{ \pi }{6} + \alpha -\frac{ \pi }{6} )]=cos^2 \alpha - \frac{1}{2}(cos \frac{ \pi }{3} +cos2 \alpha )=$ $=cos^2 \alpha - \frac{1}{2}cos \frac{ \pi }{3} - \frac{1}{2} cos2 \alpha =cos^2 \alpha - \frac{1}{2} * \frac{1}{2}- \frac{1}{2}cos2 \alpha=$ $=cos^2 \alpha - \frac{1}{4} - \frac{1}{2}(2cos^2 \alpha-1)= cos^2 \alpha - \frac{1}{4} -cos^2 \alpha+ \frac{1}{2}=- \frac{1}{4} + \frac{1}{2}= \frac{1}{4}$

P. S.
$cosx*cosy= \frac{1}{2} [cos(x-y)+cos(x+y)]$

$cos2 \alpha =2cos^2 \alpha -1$

9 votes Thanks 8

iluha23 Спасибо

Answers & Comments

Verified answer

Verified answer

3+sin2a...

2 < a<5pi...

vychislite pozhalujsta90391efd717bd520e04d497693915106 26247

sdelajte vyvody 123 zakona mendelya pozhalujsta zavtra zachet

list romashki aptechnoj chereshkovyj ili beschereshkovyj

napishite sochinenie na anglijskom yazyke na temu starye lyudi ochen odinoki i im

po teoreme vietta najdite summu i proizvedenie kornej uravneniya h2 60 x25x

рекомендуемые вопросы

Helpful Links

Helpful Social