if cos theta=1/2(x+1/x), then find the value of 1/2(x^3+1/x^3) - Maths - Trigonometric Functions

Question

if cos theta=1/2(x+1/x), then find the value of 1/2(x^3+1/x^3)
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Anuradha Sharma · Accepted Answer

Given cos θ=12x+1x, or x+1x=2cos θNow taking cube on both the side we get, x+1x3=2cos θ3x3+1x3+3×x×1xx+1x=8cos3θx3+1x3+3×2cos θ=8cos3θx3+1x3=8cos3θ-6cos θ12x3+1x3=4cos3θ-3cos θ=cos3θ

if cos theta=1/2(x+1/x), then find the value of 1/2(x^3+1/x^3) ?