Доказать 3(sin^4a+cos^4a)-2(sin^6a+cos^a)=1. Created by zhmelnyk. algebra-ru

Доказать 3(sin^4a+cos^4a)-2(sin^6a+cos^a)=1...

emerald0101 $3(sin^4 \alpha +cos^4 \alpha )-2(sin^6 \alpha +cos^6 \alpha)=1;$
$3(sin^4\alpha+cos^4\alpha)-2(sin^2\alpha+cos^2\alpha)(sin^4\alpha-sin^2\alpha cos^2\alpha+cos^4\alpha)=$
$=3(sin^4\alpha+cos^4\alpha)-2(sin^4\alpha-sin^2\alpha cos^2\alpha+cos^4\alpha)=$
$=3sin^4\alpha+3cos^4\alpha-2sin^4\alpha+2sin^2\alpha cos^2\alpha-2cos^4\alpha=$ $=sin^4\alpha+2sin^2\alpha cos^2\alpha+cos^4\alpha=(sin^2\alpha+cos^2\alpha)^2=1;$

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Lebensinhalt 3(sin^4a+cos^4a)-2(sin^6a+ cos^6a) = 3(sin^4a+cos^4a)-2(sin^2a+cos^2a)(sin^4a-sin^2a cos^2a+ cos^4a) = 3sin^4a + 3cos^4a- 2sin^4a+2sin^2a cos^2a –2cos^4a = sin^4a + 2sin^2a cos^2a+cos^4a= (sin^2a+cos^2a)^2 = 1

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