$\begin{array}{l}b) \, f(x) = y = \sin x\cos^2x + \tan x\\ Ta\,\,có: \quad\, f(-x) = \sin(-x)\cos^2(-x) + \tan(-x)\\ = -\sin x\cos^2x - \tan x\\ =-(\sin x\cos^2x + \tan x) = -f(x)\\ \Rightarrow \text{y là hàm lẻ}\\ e) \, f(x) = y = \tan x - \sin^22x\\ Ta\,\,có: \quad f(-x) = \tan(-x) - \sin2(-x)\\ = -\tan x + \sin2x\\ = -(\tan x - \sin2x) = -f(x)\\ \Rightarrow \text{y là hàm lẻ}\\ h) \, f(x) = y = 2x\sin x\\ Ta \,\,có: \quad f(x) = 2(-x)\sin(-x)\\ = -2x.(-\sin x)\\ = 2x\sin x = f(x)\\ \Rightarrow \text{y là hàm chẵn}\\ k) \, f(x) = y = 2\cos3x\\ Ta\,\,có; \quad f(-x) = 2\cos3(-x)\\ = 2\cos(-3x)\\ = 2\cos3x = f(x)\\ \Rightarrow \text{y là hàm chẵn}\\ n)\,f(x) = x^2 + \tan|x|\\ Ta\,\,có:\quad f(-x) = (-x)^2 + \tan|-x|\\ = x^2 + \tan x = f(x)\\ \Rightarrow \text{y là hàm chẵn}\end{array}$
