sinx-sin3x=cos2xsin3x Ответ : x=[tex] \frac{ \pi }{4} + \frac{ \pi }{2} ; x= \pi n[/tex]. Created by Nikmasha. algebra-ru

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Nikmasha @Nikmasha

August 2022 1 8 Report

sinx-sin3x=cos2xsin3x Ответ : x=[tex] \frac{ \pi }{4} + \frac{ \pi }{2} ; x= \pi n[/tex]

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NeZeRAvix

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$sinx-sin3x=cos2xsin3x \\ -2cos2xsinx=cos2xsin3x \\ cos2x(sin3x+2sinx)=0 \\ \\ 1) \\ cos2x=0 \\ 2x= \dfrac{ \pi }{2}+ \pi k \\ x= \dfrac{ \pi }{4}+ \dfrac{ \pi k}{2};\ k \in Z \\ \\ 2) \\ sin3x+2sinx=0 \\ 3sinx-4sin^3x+2sinx=0 \\ 5sinx-4sin^3x=0 \\ sinx(5-4sin^2x)=0 \\ \\ sinx=0 \\ x= \pi k;\ k \in Z \\ \\ 5-4sin^2x=0 \\ sin^2x= \dfrac{5}{4} \\ sinx= \dfrac{ \sqrt{5} }{2} \notin [-1;\ 1]$

Ответ: $\left [\begin{array}{I} x= \dfrac{ \pi }{4}+ \dfrac{ \pi k}{2};\ k \in Z \\x= \pi k;\ k \in Z \end{array}}$

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