Question

If $\tan\theta = - \frac{1}{\sqrt{10}}$and $\theta$ lies in the fourth quadrant, then $\cos\theta =$

• A. $1/\sqrt{11}$
• B. $- 1/\sqrt{11}$
• C. $\sqrt{\frac{10}{11}}$
• D. $- \sqrt{\frac{10}{11}}$

Answer 1

Answer: (C)

$\sqrt{\frac{10}{11}}$

Answer 2

We have $\tan\theta = - \frac{1}{\sqrt{10}},$ therefore $\theta$is in IV quadrant. So $\cos\theta = + ve$

Now $1 + \tan^{2}\theta = \sec^{2}\theta \Rightarrow 1 + \frac{1}{10} = \sec^{2}\theta$

$\Rightarrow \sec^{2}\theta = \frac{11}{10} \Rightarrow \cos\theta = \sqrt{\left( \frac{10}{11} \right)}$