Даю 60 баллов за правильный ответ !Помогите с тригонометрия ! Докажи уравнения :[tex](sin^3 \alpha +cos^3 \alpha ) / (sin \alpha +cos \alpha )+sin \alpha cos \alpha =1[/tex]. Created by chikinaeva01. algebra-ru

tex]...

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

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

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

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

$1 = 1$

MizoriesKun (sin³α+cos³α) (sinα+cosα)(sin²α-sinα*cosα+cos²α)
___________ +sinα*cosα = ____________________________ +sinα*cosα=
(sinα + cosα) (sinα + cosα)

= sin²α-sinα*cosα+cos²α +sinα*cosα = sin²α +cos²α =1

chikinaeva01 спасибо

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