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$$\cos(x) \cdot \cosh (x) + 1 = 0$$

Sorry I am a software developer and I have forgotten this part of mathematics! What is the value of $x$ in the above equation?

I need the steps to solve the equation like school level where we solve the equation!

Rather can we simplify the equation?

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5  
Numerical solutions can be given, but I seriously doubt there are any closed form solutions in x. –  Ethan Mar 28 '13 at 7:34
    
Actually I need to find value of x . What do you mean numberical solutions can be given ? Can you explain how to solve the equation with steps ? –  GuruC Mar 28 '13 at 7:37
    
There are multiple solutions, and by numerical solutions, I mean solutions that can be approximated by a finite decimal expansion, but can not be given in terms of elementary functions, for example here is one solution $x=10.9955407348...$, also note that if $x_1$ is a solution then $-x_1$ will also be a solution because $\cos(x)\cosh(x)$ is an even function. –  Ethan Mar 28 '13 at 7:39
3  
There are no specific "steps" to finding a solution to this equation, it can not be algebraically manipulated so that a series of closed form solutions can be found, it can however be approximated by various methods, for example newtons method is one. –  Ethan Mar 28 '13 at 7:44
2  
wolframalpha.com/input/… –  yiyi Mar 28 '13 at 7:52

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