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## Homework Statement

attached:

## Homework Equations

where ##J_{yz} ## is

## The Attempt at a Solution

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In a previous question have exponentiated the generator ##J_{yz}## to show it is the generator of rotation around the ##x## axis via trig expansions

so ##\Phi(t,x,y,z) \to \Phi(t,x,y cos \alpha - z sin \alpha, y sin \alpha + z cos \alpha ) ## and so via small angle expansions have:

##y \to ( y(1-\frac{\alpha^2}{2}+O(\alpha^4))-z(\alpha-\frac{\alpha^3}{3!}+O(\alpha^5))) ##

and

## z\to ( ( z(1-\frac{\alpha^2}{2}+O(\alpha^4))+y(\alpha-\frac{\alpha^3}{3!}+O(\alpha^5)))##

I am unsure now how expand. I thought perhaps a taylor expansion in multivariables - y and z- was the idea, but I can't see how you would arrive at the answer attached with this:

Any tips appreciated.ta.