The set of values of λ for which x2−λx+sin−1⁡(sin⁡4)>0 for all x∈R, is

We have,sin−1⁡(sin⁡4)=sin−1⁡(sin⁡(π−4))=π−4.∴x2−λx+sin−1⁡(sin⁡4)>0 for all x∈R⇒x2−λx+(π−4)>0 for all x∈R⇒λ2−4(π−4)<0⇒λ2+16−4π<0But, λ2+16−4π>0 for all λ∈R.So, there is no value of λ for which the given in equation holds true.