Question

довести тотожність
sin^4 alpha+cos^4 alpha = 1-2sin^2 alpha множимо на cos^2 alpha
$sin^4 a +cos^4 a=1 - 2 sin^2 a\: \times cos^2 a$
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Answer 1

Ответ:

$sin^4 \alpha+cos^4 \alpha = 1-2sin^2 \alpha \: {cos}^{2} \alpha$

$sin^4 \alpha+cos^4 \alpha - 2sin^2 \alpha {cos}^{2} \alpha + 2 { sin }^{2} \alpha {cos}^{2} \alpha = \\ = ( {sin}^{2} \alpha + {cos}^{2} \alpha {)}^{2} - 2 {sin}^{2} \alpha cos^{2} \alpha = \\ = 1 - 2 {sin}^{2} \alpha {cos}^{2} \alpha$