Решите уравнение 3ctgx+2=2tg(x-П/4). Created by vertogradskayam. algebra-ru

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vertogradskayam @vertogradskayam

July 2022 1 17 Report

Решите уравнение 3ctgx+2=2tg(x-П/4)

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$3\, ctgx+2=2\, tg(x-\frac{\pi }{4})\\\\3\cdot \frac{1}{tgx}+2=2\cdot \frac{tgx-tg\frac{\pi}{4}}{1+tgx\cdot tg\frac{\pi}{4}}\; \; ,\; \; tg\frac{\pi}{4}=1\\\\\frac{3}{tgx}+2=2\cdot \frac{tgx-1}{1+tgx}\\\\\frac{3+2tgx}{tgx}=\frac{2tgx-2}{1+tgx}\; \; ,\; \; tgx\ne 0\; ,\; \; tgx\ne -1\\\\(3+2tgx)(1+tgx)=tgx\, (2tgx-2)\\\\3+5\, tgx+2\, tg^2x=2\, tg^2x-2\, tgx\\\\7\, tgx=-3\\\\tgx=-\frac{3}{7}\\\\x=-arctg\frac{3}{7}+\pi n\; ,\; \; n\in Z$

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storona osnovaniya pravilnoj chetyrehugolnoj piramidy ravna 6 ugol mezhdu bokovo

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storona osnovaniya pravilnoj chetyrehugolnoj piramidy ravna 6 ugol mezhdu bokovo

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