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Math Help - Trigonometry proof

  1. #1
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    Trigonometry proof

    If cos^4 x/cos^2 y + sin^4 x/sin^2 y = 1, find cos^4 y/cos^2 x + sin^4 y/sin^2 x
    Sridhar
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  2. #2
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    Quote Originally Posted by yshridhar View Post
    If cos^4 x/cos^2 y + sin^4 x/sin^2 y = 1, find cos^4 y/cos^2 x + sin^4 y/sin^2 x
    Sridhar
    After simplification, you get
    cos^4(x)*sin^2(y) +sin^4(x)*cos^2(y) = sin^2(y)*cos^2(y)

    cos^4(x)*sin^2(y) +[1-cos^2(x)]^2*cos^2(y) = sin^2(y)*cos^2(y)


    cos^4(x)*sin^2(y) +[1-2cos^2(x) + cos^4(x)] *cos^2(y) = sin^2(y)*cos^2(y)

    cos^4(x)*sin^2(y) +cos^2(y)-2cos^2(x)*cos^2(y) + cos^4(x)*cos^2(y) = sin^2(y)*cos^2(y)
    cos^4(x)*[sin^2(y) +cos^2(y)]-2cos^2(x)*cos^2(y) = sin^2(y)*cos^2(y) - cos^2(y)


    cos^4(x) - 2cos^2(x)*cos^2(y) = [sin^2(y) - 1]*cos^2(y)

    cos^4(x) - 2cos^2(x)*cos^2(y) = - cos^4(y)


    cos^4(x) - 2cos^2(x)*cos^2(y) + cos^4(y) = 0

    [cos^2(x) - cos^2(y) = 0

    cos^2(x) = cos^2(y)

    1 - cos^2(x) = 1 - cos^2(y)

    sin^2(x) = sin^2(y)

    Substitute this value in the other expression and find the value.
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  3. #3
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    Thank you for the solution.
    Regards
    Sridhar
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