tex]...

July 2022 1 18 Report

Упростите:

[tex] \sqrt{1+cos2 \alpha/2 } +cos \alpha [/tex]

[tex]cos \pi /5+cos2 \pi /5+cos4 \pi /5+cos6 \pi /5[/tex]

Вычислите:

cos36*cos72

sin18*cos54

[tex] cos2 \pi /7+cos4 \pi /7+cos6 \pi /7[/tex]

Answers & Comments

Матов

Verified answer

$1)\sqrt{\frac{1+cos2a}{2}}+cosa=\sqrt{\frac{1+2cos^2a-1}{2}}+cosa=|cosa|+cosa=2cosa\\
cosa>0\\
2)cos36+cos72+cos144+cos216\\
1)cos36+cos216=2cos(144)*cos90=0\\
2)cos72+cos144=2cos(108)*cos(36)=2cos(180-72)*cos36=-2cos72*cos36=\frac{-2cos72*cos36*sin36}{sin36}=\frac{-cos72*sin72}{sin36}=\frac{-sin144}{2sin36}=\frac{-sin36}{2sin36}=-\frac{1}{2}$
$3)cos36*cos72=\frac{cos36*cos72*2sin36}{2sin36}=\frac{sin72*cos72}{2sin36}=\frac{sin144}{4sin36}=\frac{sin36}{4sin36}=\frac{1}{4}\\
4)sin18*cos54=sin18*cos(90-36)=sin18*sin36=\frac{2cos18*sin18*sin36}{2cos18}=\frac{sin36*sin36}{2cos18}$

$cos(\frac{2\pi}{7})+cos(\frac{4\pi}{7})+cos(\frac{6\pi}{7})\\
\frac{sin(\frac{\pi}{7})cos(\frac{2\pi}{7})+sin(\frac{\pi}{7})cos(\frac{4\pi}{7})+sin(\frac{\pi}{7})cos(\frac{6\pi}{7})}{sin(\frac{\pi}{7}})=-\frac{1}{2}$

1 votes Thanks 1

Answers & Comments

Verified answer

lyudi pozhalujsta pomogite s zadachami napishite hotya by odnu 1 na skolko proce

platforma shahtnogo podyomnika vesit 25 kn s kakim uskoreniem opuskaetsya podem

pomogite napisat sochinenie na anglijskom na temuhappend with me istoriya o t

dokazat chto funkciya yavlyaetsya chetnoj fh 6sin2x

ne mogu perevestiis it true that getting hurt during that fight hurt your honor

kak obnaruzhit i poluchit elektricheskij zaryad

6 g y2ctg3x

3)...

mediana ravnostoronnego treugolnika ravna 16 sm ego ploshad otnositsya k ploshad34ceb18196ca2a54f2f431a65514110e 80577

tex]...

рекомендуемые вопросы

Helpful Links

Helpful Social