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Starting from the left-hand side (LHS) of the identity
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$\frac{\sin\left(x\right)^3+\cos\left(x\right)^3}{\sin\left(x\right)+\cos\left(x\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sin(x)^3+cos(x)^3)/(sin(x)+cos(x))=1-sin(x)cos(x). Starting from the left-hand side (LHS) of the identity. Factor the sum of cubes: a^3+b^3 = (a+b)(a^2-ab+b^2). Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Simplify the fraction \frac{\left(\sin\left(x\right)+\cos\left(x\right)\right)\left(1-\sin\left(x\right)\cos\left(x\right)\right)}{\sin\left(x\right)+\cos\left(x\right)} by \sin\left(x\right)+\cos\left(x\right).