Given:
The expression is
[tex]2\cos^2(\dfrac{x}{2})-\cos (x)[/tex]
To find:
The expression which is equivalent to the given expression.
Solution:
We have,
[tex]2\cos^2(\dfrac{x}{2})-\cos (x)[/tex]
We know that,
[tex]\cos x=2\cos^2 (\dfrac{x}{2})-1[/tex]
Using this formula, the given expression can be written as
[tex]2\cos^2(\dfrac{x}{2})-\left(2\cos^2(\dfrac{x}{2})-1\right)[/tex]
[tex]=2\cos^2(\dfrac{x}{2})-2\cos^2(\dfrac{x}{2})+1[/tex]
[tex]=1[/tex]
Therefore, the given expression is equivalent to 1.
