JEE Mains · Maths · STD 11 - Trigonometrical equations
All possible values of \(\theta \in[0,2 \pi]\) for which \(\sin 2 \theta+\tan 2 \theta>0\) lie in
- A \(\left(0, \frac{\pi}{2}\right) \cup\left(\pi, \frac{3 \pi}{2}\right)\)
- B \(\left(0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \frac{3 \pi}{4}\right) \cup\left(\pi, \frac{7 \pi}{6}\right)\)
- C \(\left(0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{2}, \frac{3 \pi}{4}\right) \cup\left(\frac{3 \pi}{2}, \frac{11 \pi}{6}\right)\)
- D \(\left(0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{2}, \frac{3 \pi}{4}\right) \cup\left(\pi, \frac{5 \pi}{4}\right) \cup\left(\frac{3 \pi}{2}, \frac{7 \pi}{4}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{2}, \frac{3 \pi}{4}\right) \cup\left(\pi, \frac{5 \pi}{4}\right) \cup\left(\frac{3 \pi}{2}, \frac{7 \pi}{4}\right)\)
Step-by-step Solution
Detailed explanation
\(\sin 2 \theta+\tan 2 \theta>0\) \(\Rightarrow \sin 2 \theta+\frac{\sin 2 \theta}{\cos 2 \theta}>0\) \(\Rightarrow \sin 2 \theta \frac{(\cos 2 \theta+1)}{\cos 2 \theta}>0 \Rightarrow \tan 2 \theta\left(2 \cos ^{2} \theta\right)>0\) Note : \(\cos 2 \theta \neq 0\)…
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