provar (sin^3(x)+cos^3(x))/(sin(x)+cos(x))=1-sin(x)cos(x)

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prove sin³(x)+cos³(x)sin(x)+cos(x) =1−sin(x)cos(x)

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sin³(x)+cos³(x)sin(x)+cos(x) =1−sin(x)cos(x)

Manipulating left side

sin³(x)+cos³(x)sin(x)+cos(x)

Simplify cos³(x)+sin³(x)cos(x)+sin(x) : cos²(x)−sin(x)cos(x)+sin²(x)

=cos²(x)+sin²(x)−cos(x)sin(x)

Manipulating right side

1−sin(x)cos(x)

Rewrite using trig identities

=cos²(x)+sin²(x)−sin(x)cos(x)

We showed that the two sides could take the same form

⇒ True

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provar (sin^3(x)+cos^3(x))/(sin(x)+cos(x))=1-sin(x)cos(x)

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