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March 30, 2017

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prove that tan^2 (x/2)=1-cosx/1+cosx

  • maths - ,

    let A = x/2 , then we are proving
    tan^2 A = (1-cos(2A))/(1 + cos(2A))

    LS = sin^2 A / cos^2 A

    RS = (1 - (cos^2 A - sin^2 A) )/(1 + cos^2 A - sin^2 A)
    = (1-cos^2 A + sin^2 A) / (1-sin^2 A + cos^2 A)
    = (sin^2 A + sin^2 A)/(cos^2 A + cos^2 A)
    = 2sin^2 A / (2cos^2 A)
    = sin^2 A/cos^2 A
    = LS

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