Trigonometric EquationHard
Question
If f(x) = 
, x ≠ nπ, , then the range of values of f(x) for real values of x is-
, x ≠ nπ, , then the range of values of f(x) for real values of x is-Options
A.[-1, 3]
B.(-∞, -1]
C.(3, + ∞)
D.[-1, 3)
Solution
f(x) = 
Now 3 - 4 sin2x = y ⇒ sin2x =
but 0 < sin2x ≤ 1, ∵ sin x = 0, x = nπ
0 <
≤ 1 ⇒ 0 < 3 - y ≤ 4
-3 < - y ≤ 1 ⇒ - 1 ≤ y < 3 ⇒ [-1, 3]
Now 3 - 4 sin2x = y ⇒ sin2x =
but 0 < sin2x ≤ 1, ∵ sin x = 0, x = nπ
0 <
≤ 1 ⇒ 0 < 3 - y ≤ 4 -3 < - y ≤ 1 ⇒ - 1 ≤ y < 3 ⇒ [-1, 3]
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