Question

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

Answer 1

B

Explanation:

Answer 2

Given:

The expression is

`2\cos^2((x)/(2))-\cos (x)`

To find:

The expression which is equivalent to the given expression.

Solution:

We have,

`2\cos^2((x)/(2))-\cos (x)`

We know that,

`\cos x=2\cos^2 ((x)/(2))-1`

Using this formula, the given expression can be written as

`2\cos^2((x)/(2))-\left(2\cos^2((x)/(2))-1\right)`

`=2\cos^2((x)/(2))-2\cos^2((x)/(2))+1`

`=1`

Therefore, the given expression is equivalent to 1.