Найдите : sin²2(π+1)+cos²2(π-1)=. Created by bulararsiniu. algebra-ru

Найдите : sin²2(π+1)+cos²2(π-1)=...

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Ответ:

$sin^2\Big(2(\pi +1)\Big)+cos^2\Big(2(\pi -1)\Big)=sin^2(2\pi +2)+cos^2(2\pi -2)=\\\\=sin^22+cos^2(-2)=sin^22+cos^22=1\\\\\\\star \ \ sin^2a+cos^2a=1\ \ \ \ ,\ \ \ sin(2\pi +a)=sina\ \ ,\ \ \ cos(2\pi +a)=cosa\ \ \star \\\\\star \ \ cos(-a)=cosa\ \ \star$

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Verified answer

Ответ:

$\sin {}^{2} (2(\pi + 1)) + \cos {}^{2}( 2(\pi - 1)) = \sin {}^{2} (2\pi + 2) + \cos {}^{2} (2\pi - 2) = sin^{2}2+cos^{2}(-2)= \sin {}^{2} 2 + \cos {}^{2} 2 = 1.$