prove that

Asked by  | 16th May, 2008, 08:09: AM

Expert Answer:

cosθ+cos2θ+cos3θ=1/4

2cos2θcosθ+cos2θ=1/4

cos2θ(2cosθ+1)=1/4

(2cos2θ-1)(2cosθ+1)=1/4

4cos3θ+2cos2θ-2cosθ-5/4 = 0

let cosθ = t

16t3+8t2-8t-5 = 0

The only real root of this equation is 0.74.

hence, cosθ = 0.74

hence, θ = cos-1(0.74)

Answered by  | 16th Jul, 2008, 12:03: PM

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