Among the following functions defined on R in | vedclass

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(C) Let $f(x) = \cos^2 x + \cos^2(x + \frac{\pi}{3}) - \cos x \cdot \cos(x + \frac{\pi}{3})$.Using the identity $\cos^2 A + \cos^2 B - 2 \cos A \cos B

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$\cos^2 x + \cos^2(x + \frac{\pi}{3}) - \cos x \cdot \cos(x + \frac{\pi}{3})$

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(C) Let $f(x) = \cos^2 x + \cos^2(x + \frac{\pi}{3}) - \cos x \cdot \cos(x + \frac{\pi}{3})$.Using the identity $\cos^2 A + \cos^2 B - 2 \cos A \cos B \cos(A-B) = \sin^2(A-B)$,we simplify the expression.Alternatively,expand the terms:$f(x) = \cos^2 x + (\cos x \cos \frac{\pi}{3} - \sin x \sin \frac{\pi}{3})^2 - \cos x (\cos x \cos \frac{\pi}{3} - \sin x \sin \frac{\pi}{3})$$f(x) = \cos^2 x + (\frac{1}{2} \cos x - \frac{\sqrt{3}}{2} \sin x)^2 - \cos x (\frac{1}{2} \cos x - \frac{\sqrt{3}}{2} \sin x)$$f(x) = \cos^2 x + (\frac{1}{4} \cos^2 x + \frac{3}{4} \sin^2 x - \frac{\sqrt{3}}{2} \sin x \cos x) - \frac{1}{2} \cos^2 x + \frac{\sqrt{3}}{2} \sin x \cos x$$f(x) = (1 + \frac{1}{4} - \frac{1}{2}) \cos^2 x + \frac{3}{4} \sin^2 x = \frac{3}{4} \cos^2 x + \frac{3}{4} \sin^2 x = \frac{3}{4}(\cos^2 x + \sin^2 x) = \frac{3}{4}$.Since $f(x) = \frac{3}{4}$ for all $x \in R$,it is a constant function.

Among the following functions defined on $R$ into $R$,the constant function is

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