докажите тождество..... Created by kefgekiz. algebra-ru

докажите тождество.......

$\Big((cos2a)^{-1}+ctg\Big(\dfrac{5\pi}{2}+2a\Big)\Big)\cdot ctg\Big(\dfrac{5\pi }{4}-a\Big)=\\\\\\=\Big(\dfrac{1}{cos2a}+ctg\Big(2\pi +\dfrac{\pi}{2}+2a\Big)\Big)\cdot ctg\Big(\pi +\dfrac{\pi}{4}-a\Big)=\\\\\\=\Big(\dfrac{1}{cos2a}+ctg\Big(\dfrac{\pi}{2}+2a\Big)\Big)\cdot ctg\Big(\dfrac{\pi}{4}-a\Big)=\\\\\\=\Big(\dfrac{1}{cos2a}-tg(2a)\Big)\cdot ctg\Big(\dfrac{\pi}{4}-a\Big)=\dfrac{1-sin2a}{cos2a}\cdot \dfrac{1+tg\frac{\pi}{4}\cdot tga}{tg\frac{\pi}{4}-tga}=$

$=\dfrac{sin^2a+cos^2a-2sina\cdot cosa}{cos^2a-sin^2a}\cdot \dfrac{1+\frac{sina}{cosa}}{1-\frac{sina}{cosa}}=\\\\\\=\dfrac{(cosa-sina)^2}{(cosa-sina)(cosa+sina)}\cdot \dfrac{cosa+sina}{cosa-sina}=\dfrac{cosa-sina}{cosa+sina}\cdot \dfrac{cosa+sina}{cosa-sina}=1\\\\\\1=1$

2 votes Thanks 1

NNNLLL54

Verified answer

Ответ есть во вложении.

Удачи Вам и успехов)!

0 votes Thanks 0

Answers & Comments

Verified answer

vychislite kpd teplovogo dvigatelya esli kolichestvo teploty otdavaemoe holodiln

srochnovychislite kpd teplovogo dvigatelya esli kolichestvo teploty otdavaemoe hol

tex]...

pomogite pozhalujsta zhelatelno s obyasneniem9fac1a90f3775a7b3e875751fbe1d6b4 71865

foto99548f83bd104f0caed2ff76185398b5 96674

reshite uravneniya na fotoc5b90f33533c2e7a920624de1e2e55bc 85014

zadanie na fotobbdacc73c491fb4daea7a18624a146ab 95511

foto3915d8ed59394230e80223c476aaff82 79214

zadanie na foto092fbcb6af4b44aa53d8990df7008bc3 56529

predmet vysotoj 30sm raspolozhen na rasstoyanii 80sm ot linzy s opticheskoj siloj

рекомендуемые вопросы

Helpful Links

Helpful Social