Find the time complexity of the following recurrance relation: T(n) = T(n - 1) + sin(n) , 'n' is measured in degree(s) Options are: A) $theta$(n) B) $theta$(1) C) $theta$(logn) D) $theta$(n.logn)

Please show the ideal way to deal with such comparisons as I am getting g>=f IN genral what logic shall be followed to analyse such complex comparions?

cant we write the recurrance relation for bar() as T(n) = 5T(n-1) + c, like cant we take both the recurrance call as combined as both have same parameter? and if not, then how to solve such?