Trigonometric Prove...2

Discussion in 'Other Pre-University Math' started by nycmathguy, Jan 30, 2022.

  1. nycmathguy

    nycmathguy

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    David Cohen

    IMG_20220130_130436.jpg
     
    nycmathguy, Jan 30, 2022
    #1
  2. nycmathguy

    MathLover1

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    suppose that

    x+1/x=2cos(θ)

    show that x^3+1/x^3=2cos(3θ)

    Given,
    x+1/x=2cos(θ)

    =>(x+1/x)^3=(2cos(θ) )^3

    (x+1/x)^3=(2cos(θ) )^3

    x^3 + 1/x^3 + 3 x + 3/x=8cos^3(θ)

    x^3 + 1/x^3 + 3(x + 1/x)=8cos^3(θ) ......substitute given value for (x+1/x)
    x^3 + 1/x^3 + 3*2cos(θ)=8cos^3(θ)

    x^3 + 1/x^3 + 6cos(θ)=8cos^3(θ)

    x^3 + 1/x^3 =8cos^3(θ)-6cos(θ)

    x^3 + 1/x^3 =2cos(theta)(4cos^2(θ)-3)

    x^3 + 1/x^3 =2cos(θ)(2cos(2 θ) - 1)

    x^3 + 1/x^3 =2cos3θ.
     
    MathLover1, Jan 30, 2022
    #2
    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    I am convinced that there are no math problems you cannot solve.
     
    nycmathguy, Jan 31, 2022
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