Problem

29. \( \frac{1+\cos x}{\sin x}+\frac{\sin x}{1+\cos x}=2 \csc x \)

Answer

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Answer

Step 3: Divide by \(1+\cos x\), obtaining \(2 - \cos x = 2\csc x\)

Steps

Step 1 ：Step 1: Multiply both terms by \((1+\cos x)\), obtaining \(1 + 2\cos x + \sin^2 x = 2(1+\cos x)\csc x\)

Step 2 ：Step 2: Replace \(\sin^2 x\) with \(1 - \cos^2 x\), resulting in \(2 - \cos^2 x + 2\cos x = 2(1+\cos x)\csc x\)

Step 3 ：Step 3: Divide by \(1+\cos x\), obtaining \(2 - \cos x = 2\csc x\)

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