Step 1: Rationalize the Denominator

Multiply the numerator and the denominator inside the square root by $(1 + \cos\theta)$ to eliminate the radical in the denominator.

$\sqrt{\frac{(1+\cos\theta)(1+\cos\theta)}{(1-\cos\theta)(1+\cos\theta)}} = \sqrt{\frac{(1+\cos\theta)^2}{1-\cos^2\theta}}$

Step 2: Apply Trigonometric Identity

Use the fundamental trigonometric identity $1 - \cos^2\theta = \sin^2\theta$ in the denominator.

$\sqrt{\frac{(1+\cos\theta)^2}{\sin^2\theta}}$

Step 3: Extract Square Roots

Take the square root of both numerator and denominator.

$\frac{1 + \cos\theta}{\sin\theta}$

Step 4: Split into Standard Ratios

Express the fraction as the sum of two separate terms: $\frac{1}{\sin\theta} + \frac{\cos\theta}{\sin\theta}$.

$\csc\theta + \cot\theta$