The number of solutions of the equation sin5⁡x−cos5⁡x=1cos⁡x−1sin⁡x(sin⁡x≠cos⁡x) is

# The number of solutions of the equation ${\mathrm{sin}}^{5}\mathrm{x}-{\mathrm{cos}}^{5}\mathrm{x}=\frac{1}{\mathrm{cos}\mathrm{x}}-\frac{1}{\mathrm{sin}\mathrm{x}}\left(\mathrm{sin}\mathrm{x}\ne \mathrm{cos}\mathrm{x}\right)$ is

1. A

0

2. B

1

3. C

infinite

4. D

None of these

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