b) \( g(x)=\frac{\operatorname{sen}(x)}{\cos (2 x)} \)
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The Deep Dive
Did you know that the function \( g(x) = \frac{\sin(x)}{\cos(2x)} \) ties back to some fascinating trigonometric identities? Specifically, using the double angle formula, we know that \( \cos(2x) = \cos^2(x) - \sin^2(x) \). This means that you can rewrite this function in diverse forms, deepening your understanding of its behavior over different intervals. When working with generic trigonometric functions, a common pitfall is overlooking the domain. In this case, \( g(x) \) will be undefined whenever \( \cos(2x) = 0 \), which happens at specific \( x \) values, such as \( x = \frac{\pi}{4} + \frac{k\pi}{2} \) for any integer \( k \). Always ensure to check for these restrictions to avoid calculation errors!