Why can't cos (360-60) = cos (- 60) be equal to - cos60

Why can't cos (360-60) = cos (- 60) be equal to - cos60

Cos x = cos (- x), which can be regarded as a formula, so negative sign cannot be advanced

A calculation problem about trigonometric function. The important thing is the process
In △ ABC, angle c = 90 °, ad is the bisector of angle a, and Tan angle DAC = root 3 / 3, BD = root 3, so s △ ABC can be obtained
There is no picture in this question. The answer is 9 root 3 / 8
Basic problem. Please explain the idea of doing the problem where necessary

So BC / DC = 3, BD = root 3, BC = 3 * (root 3) / 2, AC = 3 / 2, then the area of right triangle ABC = BC * AC / 2 = 9 * (root 3) / 8