5) \( 1-\tan x \cdot \cos x \cdot \sin x \)

Did you know that the expression involves a juicy interplay between trigonometric identities? First, recall that \( \tan x = \frac{\sin x}{\cos x} \). By substituting this into your expression, you'll get \( 1 - \sin^2 x \). This connects directly with the fundamental Pythagorean identity, setting the stage for a more straightforward computation! Now, take a moment to play around with this in real-life applications! Trigonometric functions are more than just problem-solving tools in math—they're vital in fields like engineering and physics, especially when dealing with waves, oscillations, and even sound. Whether you’re designing a roller coaster or analyzing sound waves, those trigonometric identities help create functional designs and models in the real world!