Answer
a. even.
b. odd.
c. odd.
d. even.
e. even.
Work Step by Step
Given $ f $ and $ g $ are odd functions, we have $ f(-x)=-f(x)$ and $ g(-x)=-g(x)$
a. $ f(-x)g(-x)=f(x)g(x)$ would be even.
b. $ f^3(-x)=-f^3(x)$ would be odd.
c. $ f(sin(-x))=f(-sin(x))=-f(sin(x))$ would be odd.
d. $ g(sec(-x))=g(sec(x))$ would be even.
e. $|g(-x)|=|-g(x)|=|g(x)|$ would be even.
