use power reducing formulas to reduce tan^2(4x)cos^4(4x)

Answer 1

tan²(4x) = sin²(4x) / cos²(4x)

tan²(4x) cos⁴(4x)= sin²(4x) cos²(4x) = 1/4 sin²(8x) = 1/4 * (1 - cos 16x) / 2 = (1 - cos 16x) / 8