Question Number 144429 by gsk2684 last updated on 25/Jun/21
![Set a,b∈[−Π Π] be such that cos (a−b)=1 and cos (a+b)=(1/e). Then find the number of pairs of a,b satisfying the above system of equations?](Q144429.png)
$$\mathrm{Set}\:\mathrm{a},\mathrm{b}\in\left[−\Pi\:\Pi\right]\:\mathrm{be}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{cos}\:\left(\mathrm{a}−\mathrm{b}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{cos}\:\left(\mathrm{a}+\mathrm{b}\right)=\frac{\mathrm{1}}{\mathrm{e}}. \\ $$$$\mathrm{Then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{pairs} \\ $$$$\mathrm{of}\:\mathrm{a},\mathrm{b}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{above}\: \\ $$$$\mathrm{system}\:\mathrm{of}\:\mathrm{equations}? \\ $$