If `a` is any real number, the number of roots of `cotx-t a nx=a` in the first quadrant is (are). `2` (b) `0` (c) `1` (d) none of these

Explanation

`cotx - tanx = a`

`=>1/tanx - tanx = a`

`=>1-tan^2x = atanx`

`=>tan^2x+atanx - 1 =0`

It is a quadratic equation.

Discriminant of this equation,

`D = a^2 - 4(-1)(1) = a^2+4`

So, `D gt 0`.

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