The equation is:
cotg(X) = (sqrt(3)*cos(50º) + sin(50º))*(1-2*sqrt(3)*cos(50º)+2*sin(50º)) /
(sqrt(3)*sin(50º) - cos(50º))
Using a calculator, I find X = 50º.
How to develop the equation to find the solution?
Thanks.
Doing what you propose with the calculator we arrive to 50 degrees.
So, if X = 50, it would be possible to "develop" or simplify the trigonometric expression on the second member of the equation to arrive to cotg(50).
Don't you think so, considering that in the expression we have only trigonometric functions of the same angle?
Consider any angle $\displaystyle \alpha$ instead of $\displaystyle 50^0$ and expand $\displaystyle \cot \alpha$ in the following way:
$\displaystyle \cot \alpha =\cot \;[30^0+(\alpha -30^0)]=\frac{\cot 30^0\cdot \cot (\alpha -30^0)-1}{\cot 30^0+\cot (\alpha -30^0)}=$
$\displaystyle \frac{\sqrt{3}\cdot \dfrac{\cos (\alpha-30^0)}{\sin (\alpha-30^0)}-1}{\sqrt{3}+\dfrac{\cos (\alpha-30^0)}{\sin (\alpha-30^0)}}}=\ldots$
Let's see if you get the right side of the equation (with $\displaystyle \alpha$ instead of $\displaystyle 50^0$ ).
P.D. I haven't checked it, it is only a proposal.