Question

If $co\sec \theta -\cot \theta =2017$, then quadrant in which $\theta$ lies is :

• A. $I$
• B. $IV$
• C. $III$
• D. $II$

Answer 1

The correct option is D $II$

$cosec\theta -\cot \theta =2017$

$\cos ec\theta +\cot \theta =\frac{1}{2017}$ as $cose{c}^2\theta -{\cot }^2\theta =1$

$2\cos ec\theta =2017+\frac{1}{2017};\Rightarrow \sin \theta =+ve$

$2\cot \theta =\frac{1}{2017}-2017;\cot \theta =-ve,\Rightarrow \cos \theta -ve$

Thus, $\sin \theta =+ve$ and $\cos \theta -ve$ is possible only in the $II$ quadrant.

Thus the value of $\theta$ lies in the $second$ quadrant.