Final Answer
Step-by-step Solution
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Start by simplifying the right side of the identity: $\frac{\sin\left(2x\right)}{2\cos\left(x\right)^2}$
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$\frac{\sin\left(x\right)+\tan\left(x\right)}{1+\cos\left(x\right)}=\tan\left(x\right)$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sin(x)+tan(x))/(1+cos(x))=sin(2x)/(2cos(x)^2). Start by simplifying the right side of the identity: \frac{\sin\left(2x\right)}{2\cos\left(x\right)^2}. Starting from the left-hand side (LHS) of the identity. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Combine all terms into a single fraction with \cos\left(x\right) as common denominator.