If \(f(x)=\sin x\) and \(g(x)=\cos x\), what is the value of \((f^2+g^2)(x)\)? Here, \(f^2\) and \(g^2\) denote the pointwise squares of the functions.

Correct answer: \(1\)

For pointwise function operations, \((f^2+g^2)(x)=[f(x)]^2+[g(x)]^2=\sin^2 x+\cos^2 x\). Using the fundamental trigonometric identity \(\sin^2 x+\cos^2 x=1\), the value is \(1\). Option C uses subtraction, while option D is the double-angle expression \(\sin 2x\). Exam tip: immediately recognize \(\sin^2 x+\cos^2 x=1\).