(tg(a)+ctg(a))/tg(a)-ctg(a))=...Если tg(a)=2/3. Created by QiRong. algebra-ru

Ответ:Объяснение:*** При решении использованы формулы:Решение:

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QiRong @QiRong

July 2022 1 8 Report

(tg(a)+ctg(a))/tg(a)-ctg(a))=...
Если tg(a)=2/3

Answers & Comments

sergeevaolga5

Verified answer

Ответ:

$-2,6$

Объяснение:

*** При решении использованы формулы:

$tga=\frac{sina}{cosa},\;\;\;\;\;ctga=\frac{cosa}{sina}\\\\sin^2a+cos^2a=1\\cos^2a-sin^2a=cos2a\\1+tg^2a=\frac{1}{cos^2a}$

Решение:

$tga=2/3\\\\\frac{tga+ctga}{tga-ctga}=\frac{\frac{sina}{cosa}+\frac{cosa}{sina}}{\frac{sina}{cosa}-\frac{cosa}{sina}}=\frac{\frac{sin^2a+cos^2a}{sinacosa}}{\frac{sin^2a-cos^2a}{sinacosa}}=\frac{1}{sin^2a-cos^2a}=\frac{1}{1-cos^2a-cos^2a}=\\\\\\=\frac{1}{1-2cos^2a}=\frac{1}{1-\frac{2}{1+tg^2a}}=\frac{1}{\frac{1+tg^2a-2}{1+tg^2a}}=\frac{1+tg^2a}{tg^2a-1}\\\\\\\frac{1+tg^2a}{tg^2a-1}=\frac{1+(2/3)^2}{(2/3)^2-1}=\frac{1+(4/9)}{(4/9)-1}=\frac{13/9}{-5/9}=-\frac{13}{5}=-2,6$

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