If , then the value of is equal…

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

If f(x)=sin⁡(log⁡x)f(x)=\sin(\log x), then the value of f(xy)+f(xy)−2f(x)cos⁡(log⁡y)f(xy)+f\left(\frac{x}{y}\right)-2f(x)\cos(\log y) is equal to (1) 1 (2) 0 (3) −1-1 (4) sin⁡(log⁡x)cos⁡(log⁡y)\sin(\log x)\cos(\log y)

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