sec^2 210 degrees - 2 tan^2 240 degrees - cot 120 degrees

sec^2 210 degrees - 2 tan^2 240 degrees - cot 120 degrees

 

\(sec^2 210 - 2 tan^2 240- cot 120\\ =sec^2 30 - 2 tan^2 60+ cot 60\\ =cos^2 60 - 2 tan^2 60+ tan30\\ =(\frac{1}{2})^2 - 2(\frac{\sqrt3}{1})^2+ (\frac{1}{\sqrt3})\\ =\frac{1}{4} - 2*3+ (\frac{1}{\sqrt3})\\ =\frac{1}{4} - 6+ \frac{1}{\sqrt3}*\frac{\sqrt3}{\sqrt3}\\ =\frac{1}{4} - 6+\frac{\sqrt3}{3}\\ =\frac{1}{4} - \frac{24}{4}+\frac{\sqrt3}{3}\\ =\frac{\sqrt3}{3}-\frac{23}{4}\\ =\frac{4\sqrt3-69}{12}\)