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# Thread: Help me to solve this equation

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

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

5. The equation is solved. If your trying to do it in a calculator, TI-89 for example, then make sure that.

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.

6. 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.

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. Ah! Sorry. It seems you found your answer in a double post, which is aginst FK rules.

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!

9. If (x,y,r,t) are given, all those transcendental functions can just be evaluated, yielding constants. You then have a linear system/matrix equation in (a,b,c,d). It is difficult to tell if the system is nonsingular or poorly conditioned - really depends upon what values of x,y,r,t are permissible.

Assuming it's nonsingular, you could solve it using gaussian elimination & partial pivoting. That's kindof a brute force approach but it's simple. If it is singular, maybe some sort of least squares approach is appropriate.

There might be a clever change of variables that makes the solution an explicit formula but it's hard to tell. You could try using eulers formulae [ 2cos(x)=exp(ix)+exp(-ix), and so forth], maybe something simplifies/cancels? Not expecting much though.

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