Final Answer
Step-by-step Solution
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Starting from the left-hand side (LHS) of the identity
Factor the polynomial $\sin\left(x\right)+\sin\left(x\right)\cot\left(x\right)^2$ by it's greatest common factor (GCF): $\sin\left(x\right)$
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$\sin\left(x\right)+\sin\left(x\right)\cot\left(x\right)^2$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sin(x)+sin(x)cot(x)^2=csc(x). Starting from the left-hand side (LHS) of the identity. Factor the polynomial \sin\left(x\right)+\sin\left(x\right)\cot\left(x\right)^2 by it's greatest common factor (GCF): \sin\left(x\right). Apply the trigonometric identity: 1+\cot\left(\theta \right)^2=\csc\left(\theta \right)^2. Since \sin and \csc are opposite functions they cancel when multiplying.