If , , which of the following statement(s) is/are…

MATHEMATICS · Single correct · ISC · Mathematics · Sets and Functions · Compound and multiple angles

Problem

If 2f(x)+xf(1x)−2f(2sin⁡π(x+14))2f(x) + x f\left(\frac{1}{x}\right) - 2f\left(\sqrt{2} \sin \pi \left(x + \frac{1}{4}\right)\right) =4cos⁡2(πx2)+xcos⁡(πx)= 4 \cos^2\left(\frac{\pi x}{2}\right) + x \cos\left(\frac{\pi}{x}\right) , ∀x∈R−{0}\forall x \in R - \{0\} , which of the following statement(s) is/are true? (1) f(2)+f(12)=1f(2) + f\left(\frac{1}{2}\right) = 1 (2) f(2)+f(1)=0f(2) + f(1) = 0 (3) f(2)+f(1)=f(12)f(2) + f(1) = f\left(\frac{1}{2}\right) (4) f(1)⋅f(12)⋅f(2)=1f(1) \cdot f\left(\frac{1}{2}\right) \cdot f(2) = 1

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