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Combining like terms $5x$ and $-2x$
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$\lim_{x\to0}\left(\frac{\sin\left(3x\right)}{\sin\left(x\right)}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(0)lim(sin(5x-2x)/sin(x)). Combining like terms 5x and -2x. Apply the trigonometric identity: \sin\left(3\theta \right)=\sin\left(2\theta \right)\cos\left(\theta \right)+\cos\left(2\theta \right)\sin\left(\theta \right). Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right). When multiplying two powers that have the same base (\cos\left(x\right)), you can add the exponents.