# How to get to the other forms of the identity cos &#x2061;<!-- ⁡ --> 2 x =

How to get to the other forms of the identity $\mathrm{cos}2x={\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x$
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seraphinod
You can do it by using the Pythagorean identity: ${\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x=1$. This can be rewritten two different ways:
${\mathrm{sin}}^{2}x=1-{\mathrm{cos}}^{2}x$
and
${\mathrm{cos}}^{2}x=1-{\mathrm{sin}}^{2}x$
Use either of these formulas to replace the ${\mathrm{sin}}^{2}x$, or the ${\mathrm{cos}}^{2}x$, on the right side of your identity. That will give you the other two forms.