Trigonometric EquationHard
Question
Number of solutions of the equation tan x + sec x = 2cos x lying in the interval [0, 2π] is
Options
A.0
B.1
C.2
D.3
Solution
tan x + sec x = 2 cos x, x ∉ (2n + 1)
⇒ sin x + 1 = 2 cos2 x
⇒ sin x + 1 = 2(1-sin2 x)
⇒ 2sin2 x + 1sin x - 1 = 0
⇒ (2sin x -1)(sin x +1) = 0
⇒ sin x =
, sin x = - 1
⇒
of 
∴
Hence, number of solutions are two
⇒ sin x + 1 = 2 cos2 x
⇒ sin x + 1 = 2(1-sin2 x)
⇒ 2sin2 x + 1sin x - 1 = 0
⇒ (2sin x -1)(sin x +1) = 0
⇒ sin x =
, sin x = - 1⇒
of ∴
Hence, number of solutions are two
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