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Q. $\tan \left(-\frac{23 \pi}{3}\right)-\cot \left(\theta-\frac{13 \pi}{3}\right)=$

AP EAMCETAP EAMCET 2020

Solution:

$\tan \left(-\frac{23 \pi}{3}\right)-\cot \left(\theta-\frac{13 \pi}{3}\right)$
$=-\tan \left(7 \pi+\frac{2 \pi}{3}\right)+\cot \left(4 \pi+\left(\frac{\pi}{3}-\theta\right)\right)$
$=-\tan \frac{2 \pi}{3}+\cot \left(\frac{\pi}{3}-\theta\right)$
$=-\tan \left(\pi-\frac{\pi}{3}\right)+\cot \left(\frac{\pi}{3}-\theta\right)$
$=\tan \frac{\pi}{3}+\cot \left(\frac{\pi}{3}-\theta\right)=\sqrt{3}+\cot \left(\frac{\pi}{3}-\theta\right)$