Final answer to the problem
Step-by-step Solution
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Starting from the left-hand side (LHS) of the identity
Factor the polynomial $\sin\left(x\right)+\sin\left(x\right)\cos\left(x\right)$ by it's greatest common factor (GCF): $\sin\left(x\right)$
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$\frac{\sin\left(x\right)+\sin\left(x\right)\cos\left(x\right)}{1+\cos\left(x\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sin(x)+sin(x)cos(x))/(1+cos(x))=sin(x). Starting from the left-hand side (LHS) of the identity. Factor the polynomial \sin\left(x\right)+\sin\left(x\right)\cos\left(x\right) by it's greatest common factor (GCF): \sin\left(x\right). Simplify the fraction \frac{\sin\left(x\right)\left(1+\cos\left(x\right)\right)}{1+\cos\left(x\right)} by 1+\cos\left(x\right). Since we have reached the expression of our goal, we have proven the identity.