Is it Correct to Divide Both Angles by 2 in Trigonometry?

[Born2Perform]

$$cos(2x)=2cos^2(x)-1$$
what algebrical rule guarantees me thet is right to divide both angles for 2:
$$cos(x)=2cos^2(x/2)-1$$

 

[uart]

what algebrical rule ...

Substitution, nothing more.

$$cos(2x)=2cos^2(x)-1$$

Let u=2x, then

$$cos(u)=2cos^2(u/2)-1$$

Now you can replace u with whatever pronumeral you desire.

 

[tacman]

The algebraic rule that guarantees it is right to divide both angles by 2 is the double angle formula for cosine, which states that cos(2x) = 2cos^2(x) - 1. This formula is derived from the sum and difference identities for cosine and can be used to simplify trigonometric expressions involving double angles. In this case, dividing both angles by 2 allows us to use the double angle formula to rewrite the equation in a simpler form.