AP EAMCET · Maths · Trigonometric Equations
\(1+\cos ^2 \theta=3 \sin \theta \cos \theta \Rightarrow \theta=\)
- A \(n \pi+\frac{\pi}{4}, n \pi-\operatorname{Tan}^{-1}\left(\frac{1}{2}\right) ; n \in \mathbb{Z}\)
- B \(n \pi-\frac{\pi}{4}, n \pi+\operatorname{Tan}^{-1} 2 ; n \in \mathbb{Z}\)
- C \(n \pi+\frac{\pi}{4}, n \pi+\mathrm{T}\) an \(^{-1} 2 ; n \in \mathbb{Z}\)
- D \(n \pi-\frac{\pi}{4}, n \pi+\operatorname{Tan}^{-1}\left(\frac{1}{2}\right) ; n \in \mathbb{Z}\)
Answer & Solution
Correct Answer
(C) \(n \pi+\frac{\pi}{4}, n \pi+\mathrm{T}\) an \(^{-1} 2 ; n \in \mathbb{Z}\)
Step-by-step Solution
Detailed explanation
\(\frac{1+\cos ^2 \theta}{\cos ^2 \theta}=\frac{3 \sin \theta \cos \theta}{\cos ^2 \theta}\) \(\sec ^2 \theta+1=3 \tan \theta\) \(1+\tan ^2 \theta+1=3 \tan \theta\) \(\tan ^2 \theta-3 \tan \theta+2=0\) \((\tan \theta-1)(\tan \theta-2)=0\) \(\tan \theta=1\) or \(\tan \theta=2\)…
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