b) \( \frac{2}{2-2 \operatorname{sen} 30^{\circ}}-\frac{4}{4-2 \cos 60^{\prime \prime}} \)

To solve the given expression, we need to evaluate the trigonometric functions and then perform the arithmetic operations. Let's start by evaluating the sine and cosine functions. We have: - \( \sin 30^{\circ} = \frac{1}{2} \) - \( \cos 60^{\prime \prime} = \cos 60^{\circ} = \frac{1}{2} \) (Note: The angle is in degrees, not seconds) Now, let's substitute these values into the expression: \[ \frac{2}{2 - 2 \sin 30^{\circ}} - \frac{4}{4 - 2 \cos 60^{\circ}} \] \[ = \frac{2}{2 - 2 \cdot \frac{1}{2}} - \frac{4}{4 - 2 \cdot \frac{1}{2}} \] \[ = \frac{2}{2 - 1} - \frac{4}{4 - 1} \] \[ = \frac{2}{1} - \frac{4}{3} \] Now, we can perform the subtraction: \[ = 2 - \frac{4}{3} \] To subtract these fractions, we need a common denominator, which is 3: \[ = \frac{6}{3} - \frac{4}{3} \] \[ = \frac{6 - 4}{3} \] \[ = \frac{2}{3} \] So, the final answer is \( \frac{2}{3} \).