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  1. #1
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    Question Help me to solve this equation

    I do my best to solve this one , could any one help me please ,
    this is the equation
    Cosine 2x =Cosine² x -Sine² x

  2. #2
    Senior Member rachil0's Avatar
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    That's an identity, true for all arguments. (Infinitely many solutions for x).

    http://mathworld.wolfram.com/Double-AngleFormulas.html

    If you're asking how to prove it, see equations 8-11 of:

    http://mathworld.wolfram.com/Trigono...nFormulas.html

  3. #3
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    thankyou for the links but I try in many ways and it doesn't come !!!

  4. #4
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    please I need help , there is someone was help me before , I need this help again !

  5. #5
    Banned-ed-er-ing WMLeeBo's Avatar
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    The equation is solved. If your trying to do it in a calculator, TI-89 for example, then make sure that.

    1. Your in radian mode.
    2. The typed equation looks like this

    cos(2x) = (cos(x))² - (sin(x))²

    3. Also, be sure to specify that you only want values between 0>x>360. Otherwise, you will get infinitely many solutions, as previously stated by rachil0.
    Hello.

  6. #6
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    Quote Originally Posted by WMLeeBo
    The equation is solved. If your trying to do it in a calculator, TI-89 for example, then make sure that.

    1. Your in radian mode.
    2. The typed equation looks like this

    cos(2x) = (cos(x))² - (sin(x))²

    3. Also, be sure to specify that you only want values between 0>x>360. Otherwise, you will get infinitely many solutions, as previously stated by rachil0.
    I don't mean that ! I want to prove as this member proved to me in this thread

  7. #7
    Banned-ed-er-ing WMLeeBo's Avatar
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    Ah! Sorry. It seems you found your answer in a double post, which is aginst FK rules.

    Hello.

  8. #8
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    Unhappy Please help solve the system

    Please, have a look on this weird system of equations:

    a*(sinh(x)-sin(x))+b*(cosh(x)-cos(x))=c*(sinh(y)+sin(y))+d*(cosh(y)+cos(y))

    b*(sinh(x)+sin(x))+a*(cosh(x)-cos(x))=-d*(sinh(y)-sin(y))-c*(cosh(y)+cos(y))

    a*(sinh(x)+sin(x))+b*(cosh(x)+cos(x))=c*(sinh(y)-sin(y))+d*(cosh(y)-cos(y))

    b*(sinh(x)-sin(x))+a*(cosh(x)+cos(x))+d*(sinh(y)+sin(y))+c*(c osh(y)-cos(y))+r*t*[ a*(sinh(x)-sin(x))+b*(cosh(x)-cos(x))]=0

    Does anyone knows how to find a,b,c,d? (x,y,r,t are given)
    I will be very grateful for any hints!

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