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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:
4
` cot^(2) x - 2 (1 + cot^(2) x) + a^(2) = 0`
or ` cot ^(4) x - 2 cot ^(2) x + a^(2) - 2 = 0 `
` (cot^(2) x - 1)^(2) = 3 - a^(2)`
Now, for at least one solution
` 3 - a^(2) ge 0 `
or `a^(2) - 3 le 0 `
`therefore a in [ - sqrt(3), sqrt(3)] `
Integral values are - 1 , 0 , 1
`therefore ` Sum= 0
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CENGAGE-THEORY OF EQUATIONS-Exercise (Single)
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