The equation `tan^4x-2sec^2x+a=0` will have at least one solution if A) 1 < a ≤ 4 B) a ≥ 2 C) a ≤ 3 D) None of these

Options

A. `1 lt a le 4`
B. `a ge 2`
C. `a le 3`
D. none of these

Answer

C

Explanation

`tan^(4)x-2 sec^(2)x+a=0`
or `tan^(4)x-2(1+tan^(2)x)+a=0`
or `tan^(4)x-2 tan^(2) x+1=3-a`
or `(tan^(2) x-1)^(2)=3-a`
`rArr 3-a ge 0 or a le 3`