Which of the following statement(s) is/are correct? (a) Equation \( \operatorname{sgn}(x)=\sin ^...

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Which of the following statement(s) is/are correct?
(a) Equation \( \operatorname{sgn}(x)=\sin ^{-1} x \) has one solution.
(b) Equation \( \left|x^{2}-4\right| x|+3|=1 \) has six solutions.
(c) If \( \alpha \) is solution of equation \( \log _{10} x^{2}-\log _{10}(-x)=4 \), then \( \operatorname{sgn}(\alpha)=1 \)
(d) Equation \( \left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}+\left(\tan ^{-1} x\right)^{3}=3 \sin ^{-1} x \). \( \cos ^{-1} x \cdot \tan ^{-1} x \) has no solution (where \( \operatorname{sgn}(\cdot) \) denotes signum function)
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