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Factor the sum or difference of cubes using the formula: $a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2)$
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$\frac{\left(\cos\left(x\right)-\sin\left(x\right)\right)\left(\cos\left(x\right)^{2}+\cos\left(x\right)\sin\left(x\right)+\sin\left(x\right)^{2}\right)}{\cos\left(x\right)-\sin\left(x\right)}$
Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (cos(x)^3-sin(x)^3)/(cos(x)-sin(x)). Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Simplify the fraction \frac{\left(\cos\left(x\right)-\sin\left(x\right)\right)\left(1+\cos\left(x\right)\sin\left(x\right)\right)}{\cos\left(x\right)-\sin\left(x\right)} by \cos\left(x\right)-\sin\left(x\right). Simplify \cos\left(x\right)\sin\left(x\right) using the trigonometric identity: \sin(2x)=2\sin(x)\cos(x).