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Starting from the left-hand side (LHS) of the identity
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$\frac{\sin\left(x\right)+\sin\left(2x\right)}{1+\cos\left(x\right)+\cos\left(2x\right)}$
Learn how to solve problems step by step online. Prove the trigonometric identity (sin(x)+sin(2x))/(1+cos(x)cos(2x))=tan(x). Starting from the left-hand side (LHS) of the identity. Rewrite the expression 1+\cos\left(x\right)+\cos\left(2x\right) in factored form. Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right). Factor the polynomial \sin\left(x\right)+2\sin\left(x\right)\cos\left(x\right) by it's greatest common factor (GCF): \sin\left(x\right).