The AM of the roots of the equation: 4 cos ^3 x - 4 cos ^2 (pi-x) +cos x -1=0 In the interval (0,315 ) is

Answers (1)

Solution:      4 cos ^3x-4 cos ^2x+ cos x-1=0,

                       (4cos ^2-1)(cos x-1)=0

             Rightarrow       cos x=1.

            Rightarrow        x=2pi,4pi,6pi,..........100pi.

            	herefore       A.M=frac2pi(1+2+3+.....+50)50

                         A.M=frac2pi	imes 50	imes 502	imes 50=51pi.       

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