2sinx-cosx/2cosx+sinx=3 найти tgx. Created by salimovjasur2001. matematika-ru

2cosx+sinx=3 найти tgx...

salimovjasur2001 @salimovjasur2001

July 2022 1 1 Report

2sinx-cosx/2cosx+sinx=3 найти tgx

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$\frac{2\, sinx-cosx}{2\, cosx-sinx}=\Big [\, \frac{:cosx}{:cosx}\, \Big ]=\frac{2\, tgx-1}{2-tgx}=3\; \; \Rightarrow \\\\2\, tgx-1=3(2-tgx)\\\\2\, tgx-1=6-3tgx\\\\5\, tgx=5\\\\tgx=1\qquad (cosx\ne 0)$

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