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What is Cosx= 3^1/2 -1 in the form of sin^2 x

Trig identities 

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Probably there is some type mistakes in your question. A review is advised.

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Mark M. | Math Tutor--High School/College levelsMath Tutor--High School/College levels
4.9 4.9 (812 lesson ratings) (812)
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cosx = √3 - 1
 
sin2x = 1 - cos2x
 
        = 1 - (√3 - 1)2 = 1 - (3 - 2√3 + 1)
 
                               = 2√3 - 3
Kenneth S. | Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018Expert Help in Algebra/Trig/(Pre)calculu...
4.8 4.8 (62 lesson ratings) (62)
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given the specific value for cos x that you supplied, we can square that to get
cos2x = 4-2√3
 
You also know, inshallah, that cos2x = 1 - sin2x.
 
These facts should enable you to answer your question "in the form of sin2x" --whatever it means or is intended to mean.