Why is sin20 transformed into (sin10) ^ 2

(sin10) ^ 2 + (cos10) ^ 2 = 1
Sin20 degree = 2sin10 degree cos10 degree
Under root sign (1-20 degrees)
=Under the root sign (1-2sin10 degrees, cos10 degrees)
=Under the root sign [(sin10) ^ 2 + (cos10) ^ 2-2sin10 cos10] (complete square formula)
=Under the root sign (sin10 degrees - cos10 degrees) ^ 2 (cos10 degrees > sin10 degrees)
=Cos 10 degrees - Sin 10 degrees

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