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How does Cos^2 X - Sin^2 X=Cos^4 X - Sin^4 X?

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How does Cos^2 X - Sin^2 X=Cos^4 X - Sin^4 X?

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  1. sin^2 x+con^2 x=1=>

    => cos^2 x=1-sin^2 x

    first member

    cos^2 x- sin^2 x = 1-sin^2 x -sin^2 x= 1-2*sin^2 x

    second member

    cos^4 x-sin^4 x = (1-sin^2 x)^2 - sin^4 x =

    = 1 - 2*sin^2 x +sin^4 x -sin^4 x=

    =1-2*sin^2 x

    Q.E.D

    --Anna


  2. Greetings,

    Working with right hand side ...

    cos^4(x) - sin^4(x)

    = [cos^2(x) + sin^2(x)][cos^2(x) - sin^2(x)] , difference of squares

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

    = cos^2(x) - sin^2(x)

    LHS = RHS

    Regards

  3. RHS

    (cos² x - sin²x)(cos²x + sin²x)

    cos²x - sin²x

    LHS

    cos²x - sin²x

    LHS = RHS
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