# Addition Transformation identity of 1 and Cosine of Double angle

## Formula

$\large 1+\cos 2\theta = 2\cos^2 \theta$

### Proof

As per the expansion of the cosine of double angle in terms of cosine of angle.

$\cos 2 \theta = 2\cos^2 \theta -1$

$\therefore \,\,\,\,\,\,$ $1+\cos 2\theta = 2\cos^2 \theta$

It is proved that the addition of number one and cosine of double angle is equal to twice the cosine squared angle.

#### Other form

The fundamental trigonometric identity can be written as follows if the angle of the right angled triangle is $x$.

$1+\cos 2x = 2\cos^2 x$

The angle of the right angled triangle can be denoted by any symbol and the addition of $1$ and cosine of double angle is expressed as twice the square of cosine of angle.