If the function f ( x )=λ| sin x |+λ2| cos x |+ g (λ), λ ∈ R ( g is a function of λ ) is periodic with fundamental period (π/2), then

Question

If the function f ( x )=λ| sin x |+λ2| cos x |+ g (λ), λ ∈ R ( g is a function of λ ) is periodic with fundamental period (π/2), then (A) λ=0,1 (B) λ=1 (C) λ=0 (D) λ=-1

Tardigrade Admin · Accepted Answer

Q. If the function $f (x) = λ ∣ sin x ∣ + λ^{2} ∣ cos x ∣ + g (λ), λ \in R$ ( $g$ is a function of $λ$ ) is periodic with fundamental period $\frac{π}{2}$ , then

$λ = 0, 1$

$λ = 1$

$λ = 0$

$λ = - 1$

Q. If the function f(x)=λ∣sinx∣+λ2∣cosx∣+g(λ),λ∈R ( g is a function of λ ) is periodic with fundamental period 2π​, then

λ=0,1

λ=1

λ=0

λ=−1

f(2π​+x)=f(x)∀x∈R λ∣cosx∣+λ2∣sinx∣+g(λ)=λ∣sinx∣+λ2∣cosx∣+g(λ) (λ−λ2)∣cosx∣+(λ2−λ)∣sinx∣=0∀x∈R λ−λ2=0⇒λ=0,1 but λ=0 (rejected) ⇒λ=1

Q. If the function $f (x) = λ ∣ sin x ∣ + λ^{2} ∣ cos x ∣ + g (λ), λ \in R$ ( $g$ is a function of $λ$ ) is periodic with fundamental period $\frac{π}{2}$ , then

$λ = 0, 1$

$λ = 1$

$λ = 0$

$λ = - 1$