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August 2022 1 4 Report

помогите:( cos(П/2-2a), если sina=-1/корень из 5; П<a<3П/2

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Artem112

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$cos( \frac{\pi}{2}-2A )=sin2A=2sinAcosA
\\\
cosA=-\sqrt{1-sin^2A}=-\sqrt{1-( \frac{1}{ \sqrt{5} } )^2} =-\frac{2}{ \sqrt{5} }
\\\
cos( \frac{\pi}{2}-2A )=2\cdot(-\frac{1}{ \sqrt{5} })\cdot(-\frac{2}{ \sqrt{5} })=\frac{4}{5 }$

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