Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Find the number of values of x in (0, 2 π ) satisfying the equation cotx − 2 sin2x = 1.
Text Solution
Verified by ExpertsThe correct answer is:
6
(6)
cot x – 2 sin 2x = 1 ⇒ 
– 
– 1 ⇒ 1 + t 2 – 4t 2 = t + t 3 where t = tan x
⇒ t 3 + 3t 2 + t – 1 = 0 ⇒ (t + 1)(t2 + 2t – 1) = 0 ⇒ t = –1, –1 ± 
= –1, –1 – 
, –1 + 
⇒ tan x = tan 
,–tan 
, tan 
⇒ x = n π – 
, n π + 
, n π + 
– 
⇒ x = n π – 
, 
, (2n – 1) 
+ 
= n π – 
, 
+ 
.
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