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

Explanation

`tan^4x-2sec^2x +a = 0`

`=>tan^4x-2(1+tan^2x) +a = 0`

`=>tan^4x-2tan^2x -2 +a = 0`

`=>tan^4x-2tan^2x +1-3 +a = 0`

`=>(tan^2x - 1)^2 = 3-a`

To have at least one solution for this equation,

`3-a ge 0`

`=>a le 3`

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