Question

show that
12 sin^2x cos^2x = 3/2(1-cos4x)

Answer 1

2sin^2x = 1-cos2x
2cos^2x = 1+cos2x
use the above formulas to simplify

Answer 2

12 sin^2x cos^2x = 3*2sin^2x *2cos^2x
=3*(1-cos2x)(1+cos2x)
=3*(1-cos^2 2x)
=3*sin^2 2x
=3/2 * 2*sin^2 2x
=3/2 *(1-cos4x)