Published by:
CGP EDU Academic Team
Published on: August 12, 2026
The complete solution set of the equation 1 + 2 cosec x = 
is
A
2 n π − 
, n ∈ Ι
, n ∈ Ι
B
n π − 
, n ∈ Ι
, n ∈ Ι
C
2 n π + 
, n ∈ Ι
, n ∈ Ι
D
n π + 
, n ∈ Ι
, n ∈ Ι
Text Solution
Verified by ExpertsThe correct answer is:
A
1 + 2 cosec x = 
⇒ 1 + 
= 
⇒ (2 + sin x) (1 + cos x) = –sinx ⇒ 2 + 2 cos x + sin x + sin x cos x = –sin x
⇒ 2(sin x + cos x) + sin x cos x + 2 = 0
Put sin x + cos x = t ⇒ 1 + 2 sin x cos x = t 2 ∴ 2t + 
+ 2 = 0 ⇒ t 2 + 4t + 3 = 0
⇒ t = –1, –3 ⇒ sin x + cos x = –1 ⇒ cos 
= 
= cos 
⇒ x – 
= 2n π ± 
⇒ x = 2n π + π , 2n π – 
⇒ x = 2n π + π at which cosec x is not defined
∴ x = 2n π – 
.
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