Question

Exact value of : tan ${200}^{\circ }(\cot {10}^{\circ }-\tan {10}^{\circ })$ is ........................

• A. 0
• B. 1
• C. 2
• D. 4

Answer 1

The correct option is C 2

$\tan {200}^0(\cot {10}^0-\tan {10}^0)=\tan ({180}^0+{20}^0)(\frac{\cos {10}^0}{\sin {10}^0}-\frac{\sin {10}^0}{\cos {10}^0})$

$=\tan {20}^0\left(\frac{{\cos }^2{10}^0-{\sin }^2{10}^0}{\sin {10}^0\cos {10}^0}\right)=\frac{\sin {20}^0}{\cos {20}^0}\left(\frac{2\cos {20}^0}{\sin {20}^0}\right)=2$