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If the equation cof^4x-2cos e c^2x+a^2=0...

If the equation `cof^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 a. 4 b. 3 c. 2 d. 0

A

4

B

3

C

2

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
`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.
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