Trigonometric EquationEasy
Question
The number of solution of tan x + sec x = 2cos x in [0, 2π) is
Options
A.2
B.3
C.0
D.1
Solution
The given equation is tan x + sec x = 2cosx ⇒ sin x + 1 = 2cos2x
⇒ sinx + 1 = 2(1-sin2x) ⇒ 2sin2x + sinx - 1 = 0
⇒ (2 sin x - 1) (sinx + 1) = 0 ⇒ sinx =
, - 1 ⇒ x = 30o, 150o, 270o.
⇒ sinx + 1 = 2(1-sin2x) ⇒ 2sin2x + sinx - 1 = 0
⇒ (2 sin x - 1) (sinx + 1) = 0 ⇒ sinx =
, - 1 ⇒ x = 30o, 150o, 270o.Create a free account to view solution
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