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