Solve cos^3 20 - 4cos^2 20 + 3cos 20 - 4 = 0

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The discussion revolves around proving the equation √3cos(20) - sec(40) = 4, which leads to the cubic equation 2√3cos^3(20) - 8cos^2(20) - √3cos(20) + 3 = 0. Participants note that the original statement may not hold true for both radians and degrees, prompting a suggestion to verify it using a calculator. A type error is acknowledged, indicating that if the zero was meant to be a theta, the equation could be solvable. The distinction between "prove that" and "solve" is emphasized, highlighting a potential misunderstanding in the problem's requirements.
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Homework Statement


Prove that:
\sqrt{3}cos 20 - sec 40=4


The Attempt at a Solution


Assuming th statement to be true;
\sqrt{3}cos 20 - \frac{1}{2cos^{2}20 - 1}=4

2\sqrt{3}cos^{3} 20- 8 cos^{2} 20 -\sqrt{3}cos 20+3=0

It results in a cubic equation? Help
 
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Problem with this question is that it's not even true for both radians and degrees. Try it on your calc.
 


Defennder said:
Problem with this question is that it's not even true for both radians and degrees. Try it on your calc.

That is an excellent point. I hadn't even thought to try it. Duh.
 


Sorry guys it was a type error!
 


Eh, if that 0 was a theta, it looks solvable.
 


Yeah, but it reads "prove that..." and not "solve..."
 

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