I've Invented New Trig!

Geometry Level 3

sos(x)=sin2(x)cos2(x)cin(x)=cos2(x)sin2(x) \text{sos}(x)=\sin^2(x)-\cos^2(x) \\ \text{cin}(x)=\cos^2(x)-\sin^2(x)

Let us define two new trigonometric identities as shown above.

For real xx, find the minimum value of 2sos(x)cin(x) 2\text{sos}(x)\text{cin}(x).

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