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AP EAMCET · Maths · Trigonometric Equations

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

  1. A \(\sqrt{3}+\cot \theta\)
  2. B \(\sqrt{3}-\tan \left(\frac{\pi}{6}+\theta\right)\)
  3. C \(\sqrt{3}+\tan \theta\)
  4. D \(\sqrt{3}+\cot \left(\frac{\pi}{3}-\theta\right)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\sqrt{3}+\cot \left(\frac{\pi}{3}-\theta\right)\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \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…