Question

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

 

विकल्प

• $$\frac{\sqrt{5}}{\sqrt{6}}$$

   

• $$\frac{2}{\sqrt{6}}$$

   

• $$\frac{1}{2}$$

   

• $$\frac{1}{\sqrt{6}}$$

   

Answer 1

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