Докажите [tex]cos2a=2cos^2a-1[/tex]. Created by sobakazabiyaka. algebra-ru

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July 2022 2 28 Report

Докажите
[tex]cos2a=2cos^2a-1[/tex]

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$cos2a=2cos^2a-1
\\cos^2a-sin^2a=2cos^2a-1
\\cos^2a-(1-cos^2a)=2cos^2a-1
\\cos^2a-1+cos^2a=2cos^2a-1
\\2cos^2a-1=2cos^2a-1$

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NeZeRAvix

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Через формулу сложения аргументов + основное тригонометрическое тождество:
$cos2a=cos(a+a)=cosa\cdot cosa -sina \cdot sina= \\ =cos^2a-sin^2a=cos^2a-(1-cos^2a)=2cos^2a-1$

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