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All possible values of \( \theta \in[0,2 \pi] \) for which \( \sin 2 \theta+\tan 2 \theta \) \( >0 \) lie in: [JEE Ma…

Q1

All possible values of \( \theta \in[0,2 \pi] \) for which \( \sin 2 \theta+\tan 2 \theta \) \( >0 \) lie in:

[JEE Main 2021, 25 Feb (Shift 1)]

a

\(\left(0, \frac{\pi}{2}\right) \cup\left(\pi, \frac{3 \pi}{2}\right) \)

b

\( \left(0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{2}, \frac{3 \pi}{4}\right) \cup\left(\pi, \frac{5 \pi}{4}\right) \cup\left(\frac{3 \pi}{2}, \frac{7 \pi}{4}\right) \)

c

\(\left(0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \frac{3 \pi}{4}\right) \cup\left(\pi, \frac{7 \pi}{6}\right) \)

d

\(\left(0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{2}, \frac{3 \pi}{4}\right) \cup\left(\frac{3 \pi}{2}, \frac{11 \pi}{6}\right) \)

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