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help me solve: find x in cos^2x - 2 sinx cosx - sin^2x = 0

  • math -

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

    2 sin ( x ) cos ( x ) = sin ( 2 x )


    Equation :

    cos ^ 2 ( x ) - 2 sin( x ) cos( x ) -
    sin ^ 2 ( x ) = 0

    we can write like :

    cos ( 2 x ) - sin ( 2 x ) = 0 Add sin ( 2 x ) to both sides

    cos ( 2 x ) - sin ( 2 x ) + sin ( 2 x ) = 0 + sin ( 2 x )

    cos ( 2 x ) = sin ( 2 x ) Divide both sides by cos ( 2 x )

    cos ( 2 x ) / cos ( 2 x ) = sin ( 2 x ) / cos ( 2 x )

    1 = tan ( 2 x )

    tan ( 2 x ) = 1



    tan ( pi / 4 ) = 1

    Tangent is a periodic function with period pi , so :

    2 x = n pi + pi / 4

    ( n is an integer ) Divide both sides by 2

    x = n pi / 2 + pi / 8

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