0
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x_{min}=arctg3" alt="5sin^2x-2sinxcosx+cos^2x=4
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5sin^2x-2sinxcosx+cos^2x=4sin^2x+4cos^2x
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sin^2x-2sinxcosx-3cos^2x=0
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tg^2x-2tgx-3=0
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D_1=1+3=4
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tgx_1=1+2=3
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tgx_2=1-2=-1
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x_1=arctg3+ \pi n,n\in Z
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x_2=- \frac{ \pi }{4}+\pi m,m\in Z
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x_{min}>0
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x_{min}=arctg3" align="absmiddle" class="latex-formula">