Упростить выражение:Cos^2(х)+ cos^2(y)

September 2021 2 7 Report

Упростить выражение:

Cos^2(х)+ cos^2(y) - cos(х-y) cos(х+y)

farb50

Ответ:

$cos^2x+cos^2y-cos(x-y)\cdot cos(x+y)=\\\\=cos^2x+cos^2y-\dfrac{1}{2}\cdot \Big(cos(x-y+x+y)+cos(x-y-x-y)\Big)=\\\\=cos^2x+cos^2y-\dfrac{1}{2}\cdot (cos2x+cos2y)=\\\\=cos^2x+cos^2y-\dfrac{1}{2}\cdot (2cos^2x-1+2cos^2y-1)=\\\\=cos^2x+cos^2y-cos^2x-cos^2y-1=-1$

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NNNLLL54

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Объяснение:

Cos²(x)+cos²(y)-cos(x-y)•cos(x+y)=cos²x+cos²y-0,5•(cos2y+cos2x)=cos²x+cos²y-0,5•(2cos²y-1+2cos²x-1)=cos²x+cos²y-cos²y-cos²x-1=-1

Ответ: –1.

1 votes Thanks 1

farb50 Говори что именно

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