Final Answer
Step-by-step Solution
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Starting from the left-hand side (LHS) of the identity
Simplify $\frac{\sin\left(3x\right)}{\sin\left(x\right)}$ into $2\cos\left(2x\right)$
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$\frac{\sin\left(3x\right)}{\sin\left(x\right)}+\frac{-\cos\left(3x\right)}{\cos\left(x\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sin(3x)/sin(x)+(-cos(3x))/cos(x)=2. Starting from the left-hand side (LHS) of the identity. Simplify \frac{\sin\left(3x\right)}{\sin\left(x\right)} into 2\cos\left(2x\right). Simplify \frac{-\cos\left(3x\right)}{\cos\left(x\right)} into -\left(2\cos\left(2x\right)-1\right). Simplify the product -(2\cos\left(2x\right)-1).