An even function is defined as:
[tex]f(-x)=f(x)[/tex]That is, the function evaluated at the negative of its argument must be the same function. Here is a list of even trigonometric functions:
[tex]\begin{gathered} \cos (-x)=\cos (x) \\ \csc (-x)=\csc (x) \end{gathered}[/tex]The rest of the trigonometric functions are not even. Now, from A we see that the function has a sin(x) term, which is not even (the term sin²(4x) is even because any function to the square are even functions). We conclude that function A is not even.
From B, we see that there is a tan(x) term, which is not even. We conclude that function B is not even.
From C, both terms have a cosine, which is even, so function C is an even function.
From D, the cosine square term has a complex argument, so we need to explore it in depth.
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