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Simplify the expression sin³(x)+cos³(x), using trigonometric functions

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Answer to a math question Simplify the expression sin³(x)+cos³(x), using trigonometric functions

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Hermann
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$\left( \sin\left({x}\right)+\cos\left({x}\right) \right) \times \left( {\sin\left({x}\right)}^{2}-\sin\left({x}\right)\cos\left({x}\right)+{\cos\left({x}\right)}^{2} \right)$
$\left( \sin\left({x}\right)+\cos\left({x}\right) \right) \times \left( 1-\sin\left({x}\right)\cos\left({x}\right) \right)$

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