AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\tan \theta \cdot \tan \left(120^{\circ}-\theta\right) \tan \left(120^{\circ}+\theta\right)=\frac{1}{\sqrt{3}}\), then \(\theta\) is equal to
- A \(\frac{n \pi}{3}+\frac{\pi}{18}, n \in \boldsymbol{Z}\)
- B \(\frac{n \pi}{3}+\frac{\pi}{12}, n \in \boldsymbol{Z}\)
- C \(\frac{n \pi}{12}+\frac{\pi}{12}, n \in \boldsymbol{Z}\)
- D \(\frac{n \pi}{3}+\frac{\pi}{6}, n \in \boldsymbol{Z}\)
Answer & Solution
Correct Answer
(A) \(\frac{n \pi}{3}+\frac{\pi}{18}, n \in \boldsymbol{Z}\)
Step-by-step Solution
Detailed explanation
We have given, \[ \tan \theta \cdot \tan \left(120^{\circ}-\theta\right) \tan \left(120^{\circ}+\theta\right)=\frac{1}{\sqrt{3}} \] Since, we know…
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