Question

Which expression is equivalent to 2cos^2(x/2)- cos(x)? Edge 2020

Answer 1

Given:

The expression is

$2\cos^2(\dfrac{x}{2})-\cos (x)$

To find:

The expression which is equivalent to the given expression.

Solution:

We have,

$2\cos^2(\dfrac{x}{2})-\cos (x)$

We know that,

$\cos x=2\cos^2 (\dfrac{x}{2})-1$

Using this formula, the given expression can be written as

$2\cos^2(\dfrac{x}{2})-\left(2\cos^2(\dfrac{x}{2})-1\right)$

$=2\cos^2(\dfrac{x}{2})-2\cos^2(\dfrac{x}{2})+1$

$=1$

Therefore, the given expression is equivalent to 1.