All possible values of - -0- 2- - for which sin2- - tan 2- -0 lie in -

tan2θ (1+cos2θ ) gt;0 tan2θ gt;0 (∵ 1+cos2θ gt;0) 2θ∈ ( 0,π2 )∪ ( π, 3π2 )∪ (2 π ,5π2 )∪ (3π,7π2 ) ⇒ ( 0,π4 )∪ ( π2, 3π4 )∪ ( π ,5π4 )∪ ( 3π2,7π4 ) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

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

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

Suggest Corrections

Similar questions

$The number of values of θ i n [0, 2 π] t h a t s a t i s f y t h e e q u a t i o n s i n^{2} θ - c o s θ \frac{1}{4}$

Q. The number of values of θ in [0, 2π] that satisfy the equation

\sin^{2} θ - \cos θ = \frac{1}{4}

(a) 1
(b) 2
(c) 3
(d) 4

Q. All possible values of

θ \in [0, 2 π]

for which

sin 2 θ + tan 2 θ > 0

lie in :

Q. If the solutions for

θ

from the equation

{sin}^{2} θ - 2 sin θ + λ = 0

lie in

⋃ n ϵ z (2 n π - \frac{π}{6}, (2 n + 1) π + \frac{π}{6})

then the set of possible values of

λ

Q. The possible value(s) of '

θ

' satisfying the equation

{sin}^{2} θ tan θ + {cos}^{2} θ cot θ - sin 2 θ = 1 + tan θ + cot θ

, where

θ \in [0, π]

is/are

Join BYJU'S Learning Program

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

The correct option is A (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 :