Final Answer
Step-by-step Solution
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Starting from the left-hand side (LHS) of the identity
Multiply the single term $\sin\left(x\right)$ by each term of the polynomial $\left(1+\cot\left(x\right)\right)$
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$\sin\left(x\right)\left(1+\cot\left(x\right)\right)$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sin(x)(1+cot(x))=sin(x)+cos(x). Starting from the left-hand side (LHS) of the identity. Multiply the single term \sin\left(x\right) by each term of the polynomial \left(1+\cot\left(x\right)\right). Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Multiplying the fraction by \sin\left(x\right).