JEE Mains · Maths · STD 11 - Trigonometrical equations
Let \(S=\left[-\pi, \frac{\pi}{2}\right)-\left\{-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3 \pi}{4}, \frac{\pi}{4}\right\}\). Then the number of elements in the set \(=\{\theta \in S : \tan \theta(1+\sqrt{5} \tan (2 \theta))=\sqrt{5}-\tan (2 \theta)\}\) is \(...\)
- A \(0\)
- B \(5\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
\(\tan \theta+\sqrt{5} \tan 2 \theta \tan \theta=\sqrt{5}-\tan 2 \theta\) \(\tan 3 \theta=\sqrt{5}\) \(\theta=\frac{ n \pi}{3}+\frac{\alpha}{3} ; \quad \tan \alpha=\sqrt{5}\) Five solution
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