All possible values of -0-2 - for which sin 2 -tan 2 -0 lie in -

The correct option is B ( 0,π4 )∪ ( π2, 3π4 )∪ ( π ,5π4 )∪ ( 3π2,7π4 ) tan2θ (1+cos2θ ) gt;0 tan2θ gt;0 (∵ 1+cos2θ gt;0) 2θ∈ ( 0,π2 )∪ ( π, 3π2 )∪ (2 π ...

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Byju's Answer

Standard XII

Mathematics

De-Moivre's Theorem

All possible ...

Question

All possible values of $θ \in [0, 2 π]$ for which $sin 2 θ + tan 2 θ > 0$ lie in :

(0, \frac{π}{2}) \cup (π, \frac{3 π}{2})

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(0, \frac{π}{4}) \cup (\frac{π}{2}, \frac{3 π}{4}) \cup (π, \frac{5 π}{4}) \cup (\frac{3 π}{2}, \frac{7 π}{4})

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(0, \frac{π}{2}) \cup (\frac{π}{2}, \frac{3 π}{4}) \cup (π, \frac{7 π}{6})

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(0, \frac{π}{4}) \cup (\frac{π}{2}, \frac{3 π}{4}) \cup (\frac{3 π}{2}, \frac{11 π}{6})

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Solution

The correct option is B $(0, \frac{π}{4}) \cup (\frac{π}{2}, \frac{3 π}{4}) \cup (π, \frac{5 π}{4}) \cup (\frac{3 π}{2}, \frac{7 π}{4})$

$tan 2 θ (1 + cos 2 θ) > 0 tan 2 θ > 0 (∵ 1 + cos 2 θ > 0)$
$2 θ \in (0, \frac{π}{2}) \cup (π, \frac{3 π}{2}) \cup (2 π, \frac{5 π}{2}) \cup (3 π, \frac{7 π}{2})$

$\Rightarrow (0, \frac{π}{4}) \cup (\frac{π}{2}, \frac{3 π}{4}) \cup (π, \frac{5 π}{4}) \cup (\frac{3 π}{2}, \frac{7 π}{4})$

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All possible values of θ∈[0,2π] for which sin2θ+tan2θ>0 lie in :

The correct option is B (0,π4)∪(π2,3π4)∪(π,5π4)∪(3π2,7π4) tan2θ(1+cos2θ)>0tan2θ>0 (∵1+cos2θ>0) 2θ∈(0,π2)∪(π,3π2)∪(2π,5π2)∪(3π,7π2) ⇒(0,π4)∪(π2,3π4)∪(π,5π4)∪(3π2,7π4)

All possible values of $θ \in [0, 2 π]$ for which $sin 2 θ + tan 2 θ > 0$ lie in :