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

[ritwik06]

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

 

[Defennder]

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

 

[Dick]

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.

 

[ritwik06]

Sorry guys it was a type error!

 

[snipez90]

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

 

[Defennder]

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