Answer:
Odd, Even.
Step-by-step explanation:
A function is even if f(x) = f(-x) and is symmetrical about the y axis.
A function is odd if f(-x) = - f(x) and is symmetric with respect to the origin.
sin^3x / cos ^3 x
= tan^3 x.
f(x) = tan^3 (x)
f(-x) = tan^3(-x) = - tan^3 x.
So here, -f(x) = f(-x) so the function is ODD.
f(x) = 1 / sec^3 x
f(x) = cos^3 x
f(-x) = cos^3 (-x) = cos^3 x
This is an even function.
If you have a graphical calculator you'll see that the first function is symmetrical about the origin and the second is symmetrical about the y-axis.
