If f(x)=sin⁡−1x⋅cos⁡−1x⋅tan⁡−1x⋅cot⁡−1x⋅sec⁡−1x⋅csc⁡−1xf(x) = \sin^{-1} x \cdot \cos^{-1} x \cdot \tan^{-1} x \cdot \cot^{-1} x \cdot \sec^{-1} x \cdot \csc^{-1} x…

Mathematics

Problem

If f(x)=sin⁡−1x⋅cos⁡−1x⋅tan⁡−1x⋅cot⁡−1x⋅sec⁡−1x⋅csc⁡−1xf(x) = \sin^{-1} x \cdot \cos^{-1} x \cdot \tan^{-1} x \cdot \cot^{-1} x \cdot \sec^{-1} x \cdot \csc^{-1} x , then which of the following statement(s) hold(s) good? a. The graph of y=f(x)y = f(x) does not lie above xx axis b. The non-negative difference between maximum minimum value of the function y=f(x)y = f(x) is 3π664\frac{3\pi^6}{64} c. The function y=f(x)y = f(x) is not injective. d. Number of non-negative integers in the domain of f(x)f(x) is two.

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