If \(\lim _{\mathrm{x}\to {1}^{+}}\frac{(\mathrm{x}-1)(6+\mathrm{λcos}(\mathrm{x}-1))+\mathrm{μsin}(1-\mathrm{x})}{(\mat…

If \(\lim _{\mathrm{x}\to {1}^{+}}\frac{(\mathrm{x}-1)(6+\mathrm{λcos}(\mathrm{x}-1))+\mathrm{μsin}(1-\mathrm{x})}{(\mathrm{x}-1{)}^{3}}=-1\), where \(\lambda ,\mu \in \mathrm{ℝ}\), then \(\lambda +\mu\) is equal to

[JEE Main 2025, 4 Apr (Shift 1)]