16sin^2xcos^2x Use the​ power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

Answer 1

The power reducing formulae for sine and cosine:

sin²(x) = (1-cos(2x))/2

cos²(x) = (1+cos(2x))/2

16sin²(x)cos²(x) = 16*((1-cos(2x))/2)*((1+cos(2x))/2)

= 4*(1-cos²(2x))

= 4*sin²(2x)

= 2*(1-cos(4x))