TRIGONOMETRIC IDENTITIES Here is an expression which includes the sine and cosine functions. \[ \sin ^{2} x+\cos ^{2} x+4 \] Use the square identity to simplify this expression. Answer: The simplified answer is: A.

Did you know that the foundational identity \(\sin^2 x + \cos^2 x = 1\) is key in so many areas of math and physics? This nifty little relationship helps not just in simplifying expressions, but it's also crucial in navigating the complexities of wave functions in physics and the analysis of periodic phenomena! Now, when it comes to simplifying \(\sin^2 x + \cos^2 x + 4\), simply use that sneaky identity! Plugging it in, you get \(1 + 4\), which yields a tidy result of \(5\). So, the simplified answer is \(5\)! Easy peasy!