Trigonometric EquationHard
Question
Consider f(x) = cos2x(2cos2x + 3sinxcosx) + ax, where a ∈ R, Value(s) of ′a′ for which f(x) is strictly increasing for all x ∈ R can be -
Options
A.4
B.5
C.6
D.7
Solution
f(x) = 2 cos22x + 
.(2sin x cos x) cos2x + ax
⇒ f(x) = 2cos22x +
.2 sin2x cos2x + ax
⇒ f(x) = 2cos22x +
sin4x + ax
f′(x) = - 4 sin4x + 3cos4x + a ≥ 0∀ x ∈ R
⇒ a ≥ 4sin 4x - 3cos4x
⇒ a ≥ 5
.(2sin x cos x) cos2x + ax⇒ f(x) = 2cos22x +
.2 sin2x cos2x + ax⇒ f(x) = 2cos22x +
sin4x + axf′(x) = - 4 sin4x + 3cos4x + a ≥ 0∀ x ∈ R
⇒ a ≥ 4sin 4x - 3cos4x
⇒ a ≥ 5
Create a free account to view solution
View Solution FreeMore Trigonometric Equation Questions
The general solution of the trigonomrtirc equation sin x + cos x = 1 is diven by...The distance, from the origin, of the normal to the curve, x = 2 cos t + 2t sin t, y = 2 sin t − 2t cos t at t =&#...Locus of mid point of the portion between the axes of x cos α + y sin α = p where p is constant is...The sides of a triangle are sinα, cosα and for some 0 . Then the greatest angle of the triangle is...If 3 sin α = 5 sin β, then =...