cos(-альфа) 3sin^2альфа-1+cos^2альфа+(1-sinальфа)(1+sinальфа)...

July 2022 1 4 Report

Упростите выражения пожалуйста:
1)sin(-альфа)/cos^2(-альфа)-1
2)sin^2(-альфа)-1/cos(-альфа)
3sin^2альфа-1+cos^2альфа+(1-sinальфа)(1+sinальфа)

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Dимасuk

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

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

$3) sin ^{2} \alpha - 1 + cos ^{2} \alpha + (1 - sin ^{2} \alpha )(1 + sin ^{2} \alpha ) =$ $-cos ^{2} \alpha + cos ^{2} \alpha +1 - sin ^{2} \alpha = cos ^{2} \alpha$

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