Question

If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is

 

Options

• \[\frac{\sqrt{5}}{\sqrt{6}}\]

   

• \[\frac{2}{\sqrt{6}}\]

   

• \[\frac{1}{2}\]

   

• \[\frac{1}{\sqrt{6}}\]

   

Answer 1

\[\frac{\sqrt{5}}{\sqrt{6}}\]
\[\text{ In the fourth quadrant, }\cos x \text{ and }\sec x\text{ are positive . }\]
\[\cos x = \frac{1}{\sec x}\]
\[ = \frac{1}{\sqrt{\sec^2 x}}\]
\[ = \frac{1}{\sqrt{1 + \tan^2 x}}\]
\[ = \frac{1}{\sqrt{1 + \left( - \frac{1}{\sqrt{5}} \right)^2}}\]
\[ = \frac{1}{\sqrt{\frac{6}{5}}}\]
\[ = \frac{\sqrt{5}}{\sqrt{6}}\]