Question

use power reduction formula to rewrite the equation in terms of cosine: cos^2x sin^4 x

Answer 1

cos^2(x) sin^4(x) = 1/2(1 + cos(2x)) * (1/2(1 - cos(2x))^2 = 1/2(1 + cos(2x)) * 1/4(1 - 2cos(2x) + cos^2(2x)) = 1/8(1 + cos(2x))(1 - 2cos(2x) + 1/2 + 1/2cos(4x)) = 1/16(1 + cos(2x))(3 - 2cos(2x) + cos(4x)) = 1/16(3 - 2cos(2x) + cos(4x) + 3cos(2x) - 2cos^2(2x) + cos(2x)cos(4x)) = 1/16(3 + cos(2x) + cos(4x) - (1 + cos(4x)) + 1/2cos(6x) + 1/2cos(2x)) = 1/32(4 + 3cos(2x) + cos(6x))