The simplification form of the trigonometric expression 2sin²xcos²x is (1/2)sin²2x.
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a trigonometric expression:
= 2sin²xcos²x
We know,
sin2a = 2sin(a)cos(a)
= (1/2)(4sin²xcos²x)
= (1/2)(2sin(x)cos(x))²
= (1/2)sin²2x
Thus, the simplification form of the trigonometric expression 2sin²xcos²x is (1/2)sin²2x.
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