Question

If $\tan \theta =\cot \theta$, then the value of $\sec \theta$ is :

• A. $2$
• B. $1$
• C. $\frac{2}{\sqrt{3}}$
• D. $\sqrt{2}$

Answer 1

The correct option is D $\sqrt{2}$

$\tan \theta =\cot \theta$

$\Rightarrow {\tan }^2\theta =1$

$\Rightarrow \tan \theta =1$

$\Rightarrow \theta =45°$

$\therefore \sec 45°=\sqrt{2}$

Hence, the answer is $\sqrt{2}.$