if tan^2 x+sec x -a=0 has atleast one solution then complete set of values of a is

put tan²x = sec²x-1 so you get
sec²x-secx-a-1 =0 this equation has roots from either less than -1 or more than 1 so
D >= 0
but now f(1) f(-1) >=0 also necessary otherwise roots will lies between (-1,1) that not possible
here >= means more than equal to
thanks