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David Cohen
suppose that
x+1/x=2cos(θ)
show that x^2+1/x^2=2cos(3θ)
Given,
x+1/x=2cos(θ)
=>(x+1/x)^2=(2cos(θ) )^2
x^2 + 1/x^2 + 2=4cos^2(θ)
x^2 + 1/x^2 =4cos^2(θ) -2
x^2 + 1/x^2 =2(2cos^2(θ) -1)
x^2 + 1/x^2 =2cos(2 θ)