Cos2A IS NOT 2CosA

A common mistake in trigonometry is the misunderstanding that cosA can be taken apart.

What is the true meaning of this "cos"?

"cos", or cosine, is actually a trigonometrical operation on an angle producing a ratio or a number.

Here, cosine is taken as a reference for this type of mistake made.
Sine and tangent are the equivalent.

You cannot take the "cos" apart from the angle A. They must exist together as a pair "cosA".

For double angle 2A, any trigonometrical operation on it will be likewise treated.

Cos2A will be an operation of cosine on this double angle 2A.

"cos" cannot be treated as a variable, standing alone.

Thus cos2A is not to be separated into "cos" "2A" or (cos)(2)(A).

With this principles, cos2A is therefore, not equal to 2cosA, since the 2A is being operated with the function "cosine".

You may wish to pump in some numbers for the angle and try for yourself this verification.
Example: cos 2(20) and 2 cos(20).
Are they really equal?

As long as you understand what is operation (or function) and operand (or the variable operated upon), you will not have any serious problem with math.

:-)