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The sum of the roots of the equation $4 \cos^{3} x - 4 \cos^{2} x - \cos (π + x) - 1 = 0 in the in terval [0, 315] is p π$ $where p is equal to$

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Correct option is B

4cos3⁡x−4cos2⁡x+cos⁡x−1=0⇒ 4cos2⁡x+1(cos⁡x−1)=0⇒cos⁡x=1⇒x=2nπ100π<315<101π Required sum =2π+4π+…100π=2(1+2+…50)π=2×50×512π=2550π

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The sum of the roots of the equation 4cos3⁡x−4cos2⁡x−cos⁡(π+x)−1=0 in the interval [0, 315] is pπ where p is equal to

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Ready to Test Your Skills?

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The sum of the roots of the equation $4 \cos^{3} x - 4 \cos^{2} x - \cos (π + x) - 1 = 0 in the in terval [0, 315] is p π$ $where p is equal to$