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the minimum value of 8(cos2A+cosA) , where A belongs to R is

  1. the minimum value of 8(cos2A+cosA) , where A belongs to R is

Grade:11

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
essentially the equation is a quadratic in cosA
Q = 8(2cos^2A + cosA - 1)
and we have to find it’s minimum value
As leading coefficient is positive the quadratic is up parabola and hence the minimum value is at the vertex whose coordinates are (cosA,Q) (-0.5,-8)
as -0.5 lies in the range of the cosine function it’s a valid answer
Thus the minimum value is -8

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