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The sum of roots of equation 4cos^(3) (P...

The sum of roots of equation `4cos^(3) (Pi + x) – 4cos^(2)(Pi – x) + cos(Pi + x) – 1 = 0` in the interval [0,320] is `p Pi`. Then p is equal to :-

Text Solution

Verified by Experts

The correct Answer is:
`2601.00`
`4cos^(3)x - 4cos^(2)x-cosx-1 = 0`
`4 cos^(3)x + 4cos^(2)x+cosx+1 = 0`
`(4cos^(2)x+1)(cosx+1) = 0`
`cos x = -1`
`x = (2n -+ 1) Pi`
`n = 0 1 2 ………….49, 50`
`x = Pi, 3 Pi, 5Pi …………… 99 Pi , 101 Pi`
`S = Pi + 3 Pi + …………+ 101 Pi`
`S = 2601 Pi`.
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