
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

Senior Member
That's an identity, true for all arguments. (Infinitely many solutions for x).
http://mathworld.wolfram.com/DoubleAngleFormulas.html
If you're asking how to prove it, see equations 811 of:
http://mathworld.wolfram.com/Trigono...nFormulas.html

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

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

Bannededering
The equation is solved. If your trying to do it in a calculator, TI89 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.

Originally Posted by WMLeeBo
The equation is solved. If your trying to do it in a calculator, TI89 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

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

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!

Senior Member
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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