If cos⁡2π7−sin⁡2π7sin⁡2π7cos⁡2π7k=1001, then the least positive integral value of k is

we know that cos⁡θ−sin⁡θsin⁡θcos⁡θn=cos⁡nθ−sin⁡nθsin⁡nθcos⁡nθ∴cos⁡2π7−sin⁡2π7sin⁡2π7cos⁡2π7k=cos⁡2kπ7−sin⁡2kπ7sin⁡2kπ7cos⁡2kπ7=1001,     if k=7m, where m∈NHence, the least value of k is 7.