Answer:
Let u = log sin x and \[v=\sqrt{\cos \,x.}\] Then, \[\frac{du}{dx}=\cot \,\,x\] and \[\frac{dv}{dx}=-\frac{\sin \,x}{2\sqrt{\cos \,x}}\] \[\therefore \] \[\frac{du}{dv}=\frac{du/dx}{dv/dx}=-\frac{\cot x}{\frac{\sin x}{2\sqrt{\cos \,x}}}\] \[=-\,2\sqrt{\cos \,x}\cot \,x\,\text{cosec}\,x\]
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