Trigonometric EquationMedium
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]
Create a free account to view solution
View Solution FreeMore Trigonometric Equation Questions
Total number of integral values of ′n′ so that sin x (sin x + cos x) = n has at least one solution is-...If A = sin2 x + cos4 x , then for all real x...If 2 cot2 θ = cosec2 θ, then the general value of θ is -...The general value of θ satisfying the equation sin2θ − 2cosθ + = 0...If sum of all the solutions of the equation 8 cos x. cosπ6+x.cosπ6-x-12 = 1 in [0, π] is kπ, then k ...