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2-125.

y = sin2x = (sinx)(sinx)

y = sinx is an odd function. Definition of odd functions: f(−x) = −f(x) Therefore, sin(−x) = −sin(x).

Explore what y = sin2(−x) looks like:
y = sin2(−x)
= (sin(−x))(sin(−x))
=(−sinx)(−sinx)
= sin2x

Hence sin2(−x) = sin2(x).
This is the definition of an even function: f(−x) = f(x).

Test for even: f(a) = f(−a)

f(a) ≠ f(−a); not even

Test for odd: f(−a) = −f(a)...