Question: B. $\frac{1}{\sin B}$ 11. Identify a non-permissible value for $\frac{1}{\cos 2x}$

B. $\frac{1}{\sin B}$

11. Identify a non-permissible value for $\frac{1}{\cos 2x}$

Solution

To identify a non-permissible value for the expression \(\frac{1}{\cos 2x}\), we need to determine when the denominator is equal to zero, since division by zero is undefined. The expression becomes undefined when: \[ \cos 2x = 0 \] The general solutions for \(\cos 2x = 0\) are: \[ 2x = \frac{\pi}{2} + k\pi, \quad k \in \mathbb{Z} \] Solving for \(x\), we have: \[ x = \frac{\pi}{4} + \frac{k\pi}{2}, \quad k \in \mathbb{Z} \] Thus, the non-permissible values of \(x\) are of the form: \[ x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \ldots \] These are the values where \(\cos 2x = 0\).