Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2 π ] is………
Text Solution
Verified by ExpertsThe correct answer is:
0002
Ans. 0002
Sol. The given equation can be written as
sin x + 1 = 2 cos 2 x
⇒ sinx + 1 = 2 (1 – sin 2 x)
⇒ 2 sin 2 x + sin x – 1 = 0
sin x = 
= 
= 
or –1
⇒ x = 
, 
Note : sin x = –1 is not possible because tan x is given in the question
So x = ± 
is not in the domain.
Hence, the required number of solutions is 2.
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