If the equation `cot^4x-2cos e c^2x+a^2=0` has at least one solution, then the sum of all possible integral values of `a` is equal to 4 (b) 3 (c) 2 (d) 0

Options

A. 4
B. 3
C. 2
D. 0

Answer

D

Explanation

`cot^4x-2(1+cot^2x)+a^2=0`
`or cot^4x-2cot^2+a^2-2=0`
`or (cot^2x-1)^2=3-a^2`
To have at least one solution, `3-a^2ge0`
`or a^2-3le0`
`a in[-sqrt3,sqrt3]`
Integral values are -1,0,1, therefore, the sum is 0.