# Subtraction Trigonometric identity of 1 and Cosine of Double angle

## Formula

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

### Proof

According to the expansion of the cosine of double angle in terms of sine of angle.

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

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

$\therefore \,\,\,\,\,\,$ $1-\cos 2\theta = 2\sin^2 \theta$

It is proved that the subtraction of cosine of double angle from one is equal to twice the sine squared angle.

#### Other form

It is also written in other form in mathematics. If angle of the right angled triangle is $x$, then the subtraction of the cos of ange $2x$ can be transformed as the twice the square of the sine of angle $x$.

$1-\cos 2x = 2\sin^2 x$

Remember, the angle of right angled triangle can be denoted by any symbol in trigonometry but the conversion of this trigonometric identity is in same form.

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