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We study the basal-plane anisotropies of reversible magnetization and torquein a mixed state of layered d-wave superconductors based on the quasiclassicalversion of the BCS-Gor'kov theory. Both the longitudinal magnetization ($M_L$)and torque ($\tau$) show fourfold oscillations as a function of the field angle$\chi$. The relationship between the node position and the oscillatory patternsshown by $M_L$ and $\tau$ is clarified. It is also shown that the sign of the$\tau (\chi)$-oscillation does not change between $H_{c1}$ and $H_{c2}$, whilethe sign of the $M_L (\chi)$-oscillation changes. The newly obtained result for$\tau$ indicates that the torque experiment can allow us to detect the in-planeanisotropies of $H_{c2}$ even in a material with strong fluctuations such ascuprate or organic superconductors, where the $H_{c2}$ itself cannot bedetermined experimentally.Comment: 10 pages, 9 figure

Basal-Plane Magnetic Anisotropies of High-κ d-Wave Superconductors in a Mixed State: A Quasiclassical Approach