Need help simplifying expression

quantum_enhan
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The Attempt at a Solution



I'm attempting to solve a question with a few unknowns, and I managed to get it to the following form:

tanx(1-cosx)=0.25


I just can't seem to simplify it further and thus solve.. Any ideas?
 
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It is more helpful if you post the entire original question and your work so far; otherwise we can't tell whether you've made a mistake in the work leading up to this point, or indeed whether you're expected to find an exact or merely approximate solution.
 
Ok.
Find theta.
2sintheta(75)(x-1.2)=45, where x=1.2costheta
 
sorry, x=1.2/costheta
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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