1.

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 :-

Answer»


SOLUTION :`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 = 012 ………….49, 50`
`x = Pi, 3 Pi, 5Pi …………… 99 Pi , 101 Pi`
`S = Pi + 3 Pi + …………+ 101 Pi`
`S = 2601 Pi`.


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