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Question Number 144429 by gsk2684 last updated on 25/Jun/21

$$\mathrm{Set}\mathrm{a},\mathrm{b}\in [-\mathrm{\Pi }\mathrm{\Pi }]\mathrm{be}\mathrm{such}\mathrm{that}$$$$\cos (\mathrm{a}-\mathrm{b})=1\mathrm{and}\cos (\mathrm{a}+\mathrm{b})=\frac{1}{\mathrm{e}}.$$$$\mathrm{Then}\mathrm{find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{pairs}$$$$\mathrm{of}\mathrm{a},\mathrm{b}\mathrm{satisfying}\mathrm{the}\mathrm{above}$$$$\mathrm{system}\mathrm{of}\mathrm{equations}?$$

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